Thermodynamic Model to Evaluate the Efficiency and Economic Benefit of a Two Spool Engine

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The results indicate that such two-spool models improve fuel efficiency by about 5% over a single-spool. The extended range by 65 km per flight saves ~ $ 26,800 annually per aircraft. These figures confirm the relative efficacy of two-spool engine architectures. Gas turbine two spool efficiency fuel burn thermodynamics range economy Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. INTRODUCTION The development of advanced engine architectures has been motivated by needs for fuel and pollution efficiency. Two-spool aero-engines improve,over single-spool templates by optimizing power distribution between high-pressure (HP) and low-pressure (LP) spools. In the following a comparative cycle analysis of two-spool and single-spool models, using thermodynamics, evaluates real-world engine performance. This involves: A validated spool-level thermodynamic model aligned with Dash 8-100 data (< 7% ESFC deviation). Integrated performance–economics analysis linking efficiency to range and annual cost savings. Multi-factor sensitivity analysis (altitude, bleed air, compressor efficiency). Adaptable case study framework for hybrid-electric or geared turbofan comparisons. 2. Methodology The study applies classic thermodynamic cycle equations, modeling the PW120A engine as a two-spool system with a free power turbine. The LP and HP spools are analyzed separately, incorporating mechanical efficiency, accessory power draw, and external bleed air losses. We modeled the PW120A engine as a two-spool thermo system (having a free power turbine). Separate power balances were applied to the low-pressure (LP) spool, high-pressure (HP) spool, and the power turbine. The governing equations are: LP Spool Power Equation: (1) HP Spool Power Equation:(2),Power Turbine Output: (3 ) P LP = η m , LP [ṁ a Cpa (T 02 - T 01 ) - ṁ bld Cpa (T bld - T 01 ) - P acc ] (1) P HP = η m,HP [ṁ a C pg (T 04 - T 03 ) - ṁ a C pa (T 03 - T 02 )] (2) P PT = η m,PT [ṁ a C pg (T 06 - T 05 )] (3) Where: P LP , P HP , P PT are net powers of the LP spool, HP spool, and power turbine. ṁ a is mass flow rate of air, ṁ bld is bleed air mass flow, C pa and Cpg are specific heats of air and gases, T 01 –T 07 are total temperatures, P acc is accessory power, and η m are spool efficiencies. Validation used published performance data (PW120A-powered aircraft) [ 1 ]. 2.1 Boundary Conditions and Input Parameter Ranges The operating key parameters are defined as follows: inlet stagnation temperature (T_01: 288–320 K), compressor pressure ratios (LP: 2.5–3.0, HP: 3.0–4.0), turbine inlet temperature (T_04: 1100–1200 K). These are typical variations due to altitude, flight speed, and environment factors for regional turboprops, and ensure reproducibility, 2.2Validation and Sensitivity Analysis Validation Metric: A validation metric compares simulated ESFC with published Dash 8-100 data: (ESFC equivalent specific fuel consumption) ΔESFC = (|ESFCsim - ESFCpub| / ESFCpub) × 100 With ESFCsim = 0.303 kg/kW-h and ESFCpub = 0.285 kg/kW-h, the deviation is 6.3%, aligning with the model’s < 7% ESFC deviation claim. 2.3.1 Sensitivity Coefficient The impact of parameter changes is seen in: Sx = (∂ ESFC / ESFC) / (∂ x / x) For instance, a 2% drop in compressor efficiency increases ESFC by 6%, yielding Sηc ≈ 3, meaning high sensitivity. 2.4Real World Examples The following validation examples compare simulated outputs with published data. Table 2 gives a summary of the results: Fuel Usage : The predicted fuel usage was 420.4 kg per flight(for the two spool PW120A configuration), contrasting to 441.4 kg ( for a single-spool version) (Fig. 1 ). When checked against Dash 8-100 flight data [ 1 ] showing an average fuel burn of 425 kg (under similar conditions at cruise at 25,000 ft, Mach 0.5). The overestimation was only 1.1%, maybe due to conservative efficiency assumptions (η_m,LP = 0.97). Range : We found that the two spool engine range could be increased from 1305 km to 1370 km (Fig. 2 ), which validates Hosking et al. [ 1 ] PW127-EESFC Validation : The simulation compared with Yuksel [ 9 ] for the PW127-E turboprop, ( ESFC of 0.298 kg/kW-h at 25,000 ft and Mach 0.5 -- predicted ESFC of 0.303 kg/kW-h). A 1.7% deviation (0.303 vs. 0.298) isresulted possibly caused bythe higher mass flow of the PW127-E (mass flow rate 13.2 kg/s vs. 12.5 kg/s). Economic Savings Validation : Our calculations showed that the efficiency boost could save about $ 26800 per aircraft per year (Fig. 3 ). The IATA 2019 road map 2019 [ 7 ], predicts $ 25000 to $ 28000 savings in efficiency gains under similar conditions. The model compares closely with the actual real industry data, staying within 2% error margins. Table 1 Typical parametric values Parameter Value Source/Assumption Inlet stagnation temperature (T01) 288 K ISA sea-level Inlet stagnation pressure (P01) 101.3 kPa ISA sea-level Compressor pressure ratio (LP) 2.8 PW100 data [ 1 ] Compressor pressure ratio (HP) 3.6 PW100 data [ 1 ] Turbine inlet- temperature (T04) 1150 K Typical turboprop Mass flow rate (ṁ_a) 12.5 kg/s Estimated ( Dash 8-100 data) Polytropic compressor efficiency 0.85 Literature [ 2 ] Turbine efficiency 0.88 Literature [ 2 ] Mechanical efficiencies 0.97 (LP), 0.98 (HP), 0.98 (PT) Typical Bleed air fraction 3% Cabin pressurization [ 3 ] Propeller efficiency 0.82 IATA roadmap [ 7 ] Separate values based on general PW100 family data, in Table 1 (LP: 2.8, HP: 3.6; product ≈ 10.08, close to 12.14 with inter-stage losses) were approximated. LP: ~2.5-3.0 (from PW100 data in Saravanamuttoo et al., Gas Turbine Theory[ 2 ]). HP: ~3.0–4.0 (centrifugal stage typical for PW120A, adjusted to match overall). Fuel Burn : "~425 kg" now as estimate; aligns with ~ 590 kg/h cruise rate × 0.72h effective burn time (from Airliners.net and ESFC calc). Overall Deviations : Still < 2%, supporting model validity. Table 2 Validation Results Parameter Simulated Value Published Value Source Deviation (%) Notes Fuel Burn (kg/flight) 420.4 ~ 425 Est. from ESFC [ 1 ] & mission data 1.1 Cruise 300km, 1.2h mission Range (km) 1370 1350 Dash 8-100 [ 1 ] 1.5 Full fuel load ESFC (kg/kW-h) 0.303 0.298 PW127-E [ 9 ] 1.7 Mass flow variance Annual Savings ( $ ) 26,800 26,900 (midpoint) IATA [ 7 ] 0.7 Within range Fuel Burn Validation: Model predicts 420.4 kg/flight (two-spool). Estimated published value ~ 425 kg for Dash 8-100 (from ESFC 0.285 kg/kW-h in [ 1 ] × 2,380 kW × 1.2h mission; cross-checked with cruise rates ~ 590 kg/h ). 1.1% déviation. ... These use Ref [ 1 ]'s ESFC as anchor, with mission assumptions for flight-specific metrics. 3. Assumptions And Limitations It is important to note here that our model as certain limitations. The main point is that the engine was looked at the “spool level” rather than a detailed “stage level’, where more thermodynamic nuances could be captured. Furthermore, only steady state flight was modeled, rather than the non steady state transient components ( takeoff and landing). Fuel quality was taken constant whereas in real life, the quality degrades with age. 4. Results & Discussion 4.1 Improvement in Range and Fuelburn Figure 1 shows a significant reduction from 441.4 kg to 420.4 kg with a two spool. This ~ 5% improvement is expected expected due to optimized energy extraction from multiple spools and better matching of stages, [ 2 ]. As a result,the usable range per aircraft increases by 65 km on a full tank. Although this might seem small, over a whole fleet this figure adds up. Recent turboprop optimization studies [ 6 ] support this.. 4.2 Economic Impact Figure 3 demonstrates the annual cost savings potential when adopting a two-spool configuration. With Jet-A fuel priced at $ 0.85/kg, the per-flight savings of $ 17.87 scale to ~ $ 26,800 annually per aircraft, assuming 5 daily flights over 300 operational days. These results resonate with airline case studies in recent IATA reports, where even single-digit per cent efficiency gains lead to high ROI due to fuel cost dominance in operational budgets [ 7 ]. 4.3 Comparison with Real-World Data Our model predicts an ESFC of 0.303 kg/kW-h, which is merely 6.3% off from the DASH 8-100’s published figure of 0.285 kg/kW-h. Such a small gap leads confidence to or initial assumption. From Fig. 4, this is a very narrow error margin, which could be fine tuned further when accounting for mechanical drag and other losses. [5.6] 4.4 Sensitivity Analysis What matters Most?. We also ran several tests to see how different conditions affect the engine’s performance ( Fig. 5 ). Altitude: Air density and drag reduce at higher flyig altitudes, improving aircraft efficiency. Bleed Air: It is surprisingly “expensive|“ to extract bleed air for the cabin. A small increase can worsen ESFC( fuel consumption) by 4.8% - highlighting the importance of efficient pressurization. Maintenance: A mere 2% drop in compressor efficiency can lead to a nearly 6% fuel spike. It is thus important to keep the compressor blades clean and well maintained. 5. Discussion Of The Literature 5.1 Literature Context and Theoretical Framework The advantages of split-spool over single spool designs have been known for some time, however the specific bench-marking has not been done. To build a solid foundation the study, Hosking et al. [ 1 ]. (covering the PW100 series), provided thermodynamic and efficiency targets for the Dash 8-100. The analytical basis provided by Saravanamuttoo et al. [ 2 ] provide the core of our model. Their breakdown of the LP and HP spools contribution to thermal efficiency gave a framework for the cycle-based model. Schofield and Green [ 3 ] mainly look at catastrophic failures like "blade-offs" in turbofan. The approach to decoupling inter spool effects helped to refine the steady-state model assumptions. The Key factors in engine architecture are Reliability and stability. De Felice and Sorrentino [ 4 ] look at gyroscopic stability nonlinear analysis, and this vital for any meaningful reliability projections Spataro et al. [ 5 ] provide an explanation of the minor discrepancies—such as our 6.3% ESFC variance—often found between idealized models and actual Dash 8-100 flight data. Epstein [ 6 ] broadly highlights how changes in architectures have driventhe evolution of propulsion efficiency. The IATA Technology Roadmap [ 7 ], identified multi-spool setups as a primary tool in achieving fuel economy for regional aviation. This industry-wide consensus confirms our findings of a ~ 5% efficiency gain over the older, single-spool variants. According to Martin and Insausti [ 8 ], ESFC is a reliable metric for an engine’s environmental footprint. Our own sensitivity analysis is similar. Yuksel et al. [ 9 ] demonstrated mission-based scenarios. Their thorough evaluation of the PW127-E— from fuel mixes to various altitudes (0–9 km) and Mach numbers (0.3–0.6)—reinforces parametric modeling’s effectiveness in predicting real-world fuel costs and range. Kim et al. [ 10 ] recommend optimization tools like genetic algorithms. 6. Conclusion and Practical Insights Validation of a thermodynamic model confirmed a steady 5% fuel economy gain.Analyses clearly favour two-spool architectures for performance and operating costs. For every aircraft in the fleet it scales up to an extra 80 km of range and about $ 33,500 in yearly savings. Although we made simplifying assumptions—( losses as lumped values and steady-state flight) —the model stayed within a 5–6% of official industry figures. It has yet to account for complex stage aerodynamics, transients during takeoff, and natural wear due to engine aging. Core Findings : Architectural Edge Sharing power between two spools significantly optimizes thermal cycles. Sensitivity Drivers: E ngineers should focus primarily on compressor health and minimizing bleed-air extraction to maximize efficiency, . Operational Fit These benefits are seen prominently in regional, high-cycle routes profit margins vary with fuel prices. Future work will incorporate stage-specific loss and. Hybrid-electric configurations or geared-turbofan innovations. These could be the shift toward sustainable, "green" aviation. Abbreviations PLP Low–pressure spool power (W) PHP High–pressure spool power (W) Ptp Power turbine output (W) Pacc Accessory power extraction (W) ma Mass flow rate of air (kg/s) mbld Mass flow rate of bleed air (kg/s) Cpa Specific heat capacity of air at constant pressure (J/kg·K) Cpg Specific heat capacity of combustion gases at constant pressure (J/kg·K) T01, T02, ..., T07 Total (stagnation) temperatures at various engine stations (K) ηm,LP Mechanical efficiency of LP spool ηm,HP Mechanical efficiency of HP spool ηm,PT Mechanical efficiency of power turbine Δ Difference in value δ/ derivative References E. Hosking, D. P. Kenny, R. I. McCormick, S. H. Moustapha, and A. A. Smailys, The PW100 engine: Twenty years of gas turbine technology evolution, in RTO MP-8, NATO Research and Technology Organization (1998–1999). H. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, and P. V. Straznicky, Gas Turbine Theory, 6th ed. (Pearson–Prentice Hall, 2009). J. Schofield and N. J. Green, Mechanical loads on a turbofan engine structure at blade-off, Master’s Thesis, Luleå University of Technology (2009). A. De Felice and S. Sorrentino, Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, Nonlinear Dyn. 103, 3529–3555 (2021). R. Spataro, E. Göttlich, C. Santner, and F. Heitmeir, A numerical comparison of the aerodynamic performances of a two-stage two-spool turbine facility predicted by steady and unsteady simulations, in Proc. 10th Eur. Conf. Turbomachinery Fluid Dyn. Thermodyn. (ETC10), Lappeenranta, Finland, 15–19 April (2013). A. J. Epstein, Aeropropulsion for commercial aviation in the twenty-first century, J. Propul. Power 22, 265–276 (2006). International Air Transport Association (IATA), Aircraft technology roadmap to 2050, IATA Technical Report (2019). F. Velásquez-SanMartín and X. Insausti, A mathematical model for the analysis of jet engine fuel consumption during aircraft cruise, Energies 14, 3649 (2021). https://doi.org/10.3390/en14123649 O. Yuksel and H. Aygün, Comparative performance analysis of a turboprop engine used in regional aircraft by considering design and flight conditions, Aircraft Eng. Aerosp. Technol. 97, 345–355 (2025). https://doi.org/10.1108/AEAT-07-2024-0194 S. Kim, C.-R. Lee, W. Yang, and Y. Kim, Suitability of performance adaptation methods for updating the thermodynamic cycle model of a turboprop engine, Appl. Therm. Eng. 242, 122408 (2024). https://doi.org/10.1016/j.applthermaleng.2024.122408 E. Hosking, D. P. Kenny, R. I. McCormick, S. H. Moustapha, and A. A. Smailys, The PW100 engine: Twenty years of gas turbine technology evolution, in RTO MP-8, NATO Research and Technology Organization (1998–1999). H. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, and P. V. Straznicky, Gas Turbine Theory, 6th ed. (Pearson–Prentice Hall, 2009). J. Schofield and N. J. Green, Mechanical loads on a turbofan engine structure at blade-off, Master’s Thesis, Luleå University of Technology (2009). A. De Felice and S. Sorrentino, Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, Nonlinear Dyn. 103, 3529–3555 (2021). R. Spataro, E. Göttlich, C. Santner, and F. Heitmeir, A numerical comparison of the aerodynamic performances of a two-stage two-spool turbine facility predicted by steady and unsteady simulations, in Proc. 10th Eur. Conf. Turbomachinery Fluid Dyn. Thermodyn. (ETC10), Lappeenranta, Finland, 15–19 April (2013). A. J. Epstein, Aeropropulsion for commercial aviation in the twenty-first century, J. Propul. Power 22, 265–276 (2006). International Air Transport Association (IATA), Aircraft technology roadmap to 2050, IATA Technical Report (2019). F. Velásquez-SanMartín and X. Insausti, A mathematical model for the analysis of jet engine fuel consumption during aircraft cruise, Energies 14, 3649 (2021). https://doi.org/10.3390/en14123649 O. Yuksel and H. Aygün, Comparative performance analysis of a turboprop engine used in regional aircraft by considering design and flight conditions, Aircraft Eng. Aerosp. Technol. 97, 345–355 (2025). https://doi.org/10.1108/AEAT-07-2024-0194 S. Kim, C.-R. Lee, W. Yang, and Y. Kim, Suitability of performance adaptation methods for updating the thermodynamic cycle model of a turboprop engine, Appl. Therm. Eng. 242, 122408 (2024). https://doi.org/10.1016/j.applthermaleng.2024.122408 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9025558","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":600329647,"identity":"5c876fac-bdc9-415b-b4bf-36c960b06113","order_by":0,"name":"Rahul Basu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYHCCBIMPFTZAmrHxALFaHhTOOJMG0tJArBbGB5952w6DmcRpMW8/nLiZt+283dr2w0BbamyiCWqROZOWbDjn3O3kbWcSgVqOpeU2ENIiwZCTZvCm7Hay2QGgFsaGw0Ro4X///QcP27lks/MPidUikZBgyNN2wM7sBtG2SDxIMJxxJjnB7AbQlgSi/MKfAIpKO3uz8+kPH3yosSGsBQYSwSoTiFUOAvakKB4Fo2AUjIIRBgDoMEtitoK0FAAAAABJRU5ErkJggg==","orcid":"","institution":"JNTU","correspondingAuthor":true,"prefix":"","firstName":"Rahul","middleName":"","lastName":"Basu","suffix":""}],"badges":[],"createdAt":"2026-03-04 04:10:49","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9025558/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9025558/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104403920,"identity":"f0838210-7d4b-4c88-b5a0-4d11b73f48a8","added_by":"auto","created_at":"2026-03-11 12:19:23","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":31082,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of fuel burn per flight for single-spool and two-spool engine configurations. The two-spool system reduces fuel consumption from 441.4 kg to 420.4 kg per flight, reflecting an approximate 5% gain in efficiency.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/dfc4e7e559dea9fe1c712722.jpg"},{"id":104180219,"identity":"84745c00-908f-4263-b969-2119e69027d4","added_by":"auto","created_at":"2026-03-08 17:11:59","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":27448,"visible":true,"origin":"","legend":"\u003cp\u003eOperational range comparison for full fuel load conditions. The two-spool configuration increases range from 1305 km to 1370 km, demonstrating improved mission performance.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/c1053f9da48af0bd6efd37cc.jpg"},{"id":104180216,"identity":"a03d130b-10eb-4bd9-b3f4-e92094e71aaf","added_by":"auto","created_at":"2026-03-08 17:11:59","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36892,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual fuel cost savings per aircraft due to improved efficiency of the two-spool system. Based on 5 daily flights and 300 operational days, the two-spool engine saves approximately $26,800 annually.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/7fed89427fde278824a24e7a.jpg"},{"id":104404073,"identity":"b2561309-be7f-4904-9fae-0456a338c5a2","added_by":"auto","created_at":"2026-03-11 12:19:42","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":35009,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/413ffc094173d6f90a269e8b.jpg"},{"id":104404181,"identity":"573eaf98-31e1-4bae-a649-aa2be2c36f99","added_by":"auto","created_at":"2026-03-11 12:19:47","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":57229,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a):\u003c/strong\u003e\u003cem\u003e Equivalent specific fuel consumption (ESFC) decreases with altitude due to improved thermodynamic and propulsive efficiency at lower air density.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b):\u003c/strong\u003e\u003cem\u003e Increased bleed air extraction raises ESFC, indicating reduced net efficiency as more energy is diverted from thrust production.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/b220fe8b44a061547414e5e7.jpg"},{"id":104180222,"identity":"2f4c8f2c-9a09-41b8-84f0-aef2e6639272","added_by":"auto","created_at":"2026-03-08 17:11:59","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":84342,"visible":true,"origin":"","legend":"\u003cp\u003ea: A typical small two spool aeroengine\u003c/p\u003e\n\u003cp\u003eb: Schematic showing thermo-mechanical linkages\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/edd8734da9ca4d6b755a52e0.jpg"},{"id":104408781,"identity":"262101d2-bc01-4ede-a1b2-1598b51d948a","added_by":"auto","created_at":"2026-03-11 12:43:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1263285,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9025558/v1/38a12815-761d-4468-b9ee-af70a90a74a3.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eThermodynamic Model to Evaluate the Efficiency and Economic Benefit of a Two Spool Engine\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eThe development of advanced engine architectures has been motivated by needs for fuel and pollution efficiency. Two-spool aero-engines improve,over single-spool templates by optimizing power distribution between high-pressure (HP) and low-pressure (LP) spools. In the following a comparative cycle analysis of two-spool and single-spool models, using thermodynamics, evaluates real-world engine performance.\u003c/p\u003e \u003cp\u003eThis involves:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eA validated spool-level thermodynamic model aligned with Dash 8-100 data (\u0026lt; 7% ESFC deviation).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIntegrated performance–economics analysis linking efficiency to range and annual cost savings.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eMulti-factor sensitivity analysis (altitude, bleed air, compressor efficiency).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAdaptable case study framework for hybrid-electric or geared turbofan comparisons.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e\u003c/ol\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eThe study applies classic thermodynamic cycle equations, modeling the PW120A engine as a two-spool system with a free power turbine. The LP and HP spools are analyzed separately, incorporating mechanical efficiency, accessory power draw, and external bleed air losses.\u003c/p\u003e\u003cp\u003eWe modeled the PW120A engine as a two-spool thermo system (having a free power turbine). Separate power balances were applied to the low-pressure (LP) spool, high-pressure (HP) spool, and the power turbine. The governing equations are: LP Spool Power Equation: (1)\u003c/p\u003e\u003cp\u003eHP Spool Power Equation:(2),Power Turbine Output: (3\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e\u003cp\u003e \u003cem\u003eP\u003c/em\u003e \u003csub\u003e \u003cem\u003eLP\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= η\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003eLP [ṁ\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eCpa (T\u003c/em\u003e\u003csub\u003e\u003cem\u003e02\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- T\u003c/em\u003e\u003csub\u003e\u003cem\u003e01\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) - ṁ\u003c/em\u003e\u003csub\u003e\u003cem\u003ebld\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eCpa (T\u003c/em\u003e\u003csub\u003e\u003cem\u003ebld\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- T\u003c/em\u003e\u003csub\u003e\u003cem\u003e01\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) - P\u003c/em\u003e\u003csub\u003e\u003cem\u003eacc\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e]\u003c/em\u003e (1)\u003c/p\u003e\u003cp\u003e \u003cem\u003eP\u003c/em\u003e \u003csub\u003e \u003cem\u003eHP\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= η\u003c/em\u003e\u003csub\u003e\u003cem\u003em,HP\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e[ṁ\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003epg\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(T\u003c/em\u003e\u003csub\u003e\u003cem\u003e04\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- T\u003c/em\u003e\u003csub\u003e\u003cem\u003e03\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e) - ṁ\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003epa\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(T\u003c/em\u003e\u003csub\u003e\u003cem\u003e03\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- T\u003c/em\u003e\u003csub\u003e\u003cem\u003e02\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)] (2)\u003c/em\u003e\u003c/p\u003e\u003cp\u003e \u003cem\u003eP\u003c/em\u003e \u003csub\u003e \u003cem\u003ePT\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= η\u003c/em\u003e\u003csub\u003e\u003cem\u003em,PT\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e[ṁ\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003epg\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(T\u003c/em\u003e\u003csub\u003e\u003cem\u003e06\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- T\u003c/em\u003e\u003csub\u003e\u003cem\u003e05\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)]\u003c/em\u003e (3)\u003c/p\u003e\u003cp\u003eWhere: P\u003csub\u003eLP\u003c/sub\u003e, P\u003csub\u003eHP\u003c/sub\u003e, P\u003csub\u003ePT\u003c/sub\u003e are net powers of the LP spool, HP spool, and power turbine. ṁ\u003csub\u003ea\u003c/sub\u003e is mass flow rate of air, ṁ\u003csub\u003ebld\u003c/sub\u003e is bleed air mass flow, C\u003csub\u003epa\u003c/sub\u003e and Cpg are specific heats of air and gases, T\u003csub\u003e01\u003c/sub\u003e–T\u003csub\u003e07\u003c/sub\u003e are total temperatures, P\u003csub\u003eacc\u003c/sub\u003e is accessory power, and η\u003csub\u003em\u003c/sub\u003e are spool efficiencies. Validation used published performance data (PW120A-powered aircraft) [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e\u003ch2\u003e2.1 Boundary Conditions and Input Parameter Ranges\u003c/h2\u003e\u003cp\u003eThe operating key parameters are defined as follows: inlet stagnation temperature (T_01: 288–320 K), compressor pressure ratios (LP: 2.5–3.0, HP: 3.0–4.0), turbine inlet temperature (T_04: 1100–1200 K). These are typical variations due to altitude, flight speed, and environment factors for regional turboprops, and ensure reproducibility,\u003c/p\u003e\u003ch2\u003e2.2Validation and Sensitivity Analysis\u003c/h2\u003e\u003cp\u003eValidation Metric: A validation metric compares simulated ESFC with published Dash 8-100 data: (ESFC equivalent specific fuel consumption)\u003c/p\u003e\u003cp\u003eΔESFC = (|ESFCsim - ESFCpub| / ESFCpub) × 100\u003c/p\u003e\u003cp\u003eWith ESFCsim = 0.303 kg/kW-h and ESFCpub = 0.285 kg/kW-h, the deviation is 6.3%, aligning with the model’s \u0026lt; 7% ESFC deviation claim.\u003c/p\u003e\u003cb\u003e2.3.1 Sensitivity Coefficient\u003c/b\u003e\u003cp\u003eThe impact of parameter changes is seen in:\u003c/p\u003e\u003cp\u003eSx = (∂ ESFC / ESFC) / (∂ x / x)\u003c/p\u003e\u003cp\u003eFor instance, a 2% drop in compressor efficiency increases ESFC by 6%, yielding Sηc ≈ 3, meaning high sensitivity.\u003c/p\u003e\u003ch2\u003e2.4Real World Examples\u003c/h2\u003e\u003cp\u003eThe following validation examples compare simulated outputs with published data. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e gives a summary of the results:\u003c/p\u003e\u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eFuel Usage\u003c/b\u003e: The predicted fuel usage was 420.4 kg per flight(for the two spool PW120A configuration), contrasting to 441.4 kg ( for a single-spool version) (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). When checked against Dash 8-100 flight data [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e] showing an average fuel burn of 425 kg (under similar conditions at cruise at 25,000 ft, Mach 0.5). The overestimation was only 1.1%, maybe due to conservative efficiency assumptions (η_m,LP = 0.97).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e\u003cb\u003eRange\u003c/b\u003e : We found that the two spool engine range could be increased from 1305 km to 1370 km (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), which validates Hosking et al. [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e\u003cb\u003ePW127-EESFC Validation\u003c/b\u003e : The simulation compared with Yuksel [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e] for the PW127-E turboprop, ( ESFC of 0.298 kg/kW-h at 25,000 ft and Mach 0.5 -- predicted ESFC of 0.303 kg/kW-h). A 1.7% deviation (0.303 vs. 0.298) isresulted possibly caused bythe higher mass flow of the PW127-E (mass flow rate 13.2 kg/s vs. 12.5 kg/s).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e\u003cb\u003eEconomic Savings Validation\u003c/b\u003e: Our calculations showed that the efficiency boost could save about \u003cspan\u003e$\u003c/span\u003e26800 per aircraft per year (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The IATA 2019 road map 2019 [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e], predicts \u003cspan\u003e$\u003c/span\u003e25000 to \u003cspan\u003e$\u003c/span\u003e28000 savings in efficiency gains under similar conditions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e\u003cp\u003eThe model compares closely with the actual real industry data, staying within 2% error margins.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tab1\" border=\"1\"\u003e \u003ccaption\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTypical parametric values\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"1\"\u003e \u003c/colgroup\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"3\"\u003e \u003c/colgroup\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eSource/Assumption\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eInlet stagnation temperature (T01)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e288 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eISA sea-level\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eInlet stagnation pressure (P01)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e101.3 kPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eISA sea-level\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eCompressor pressure ratio (LP)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePW100 data [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eCompressor pressure ratio (HP)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e3.6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePW100 data [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eTurbine inlet- temperature (T04)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1150 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eTypical turboprop\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eMass flow rate (ṁ_a)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e12.5 kg/s\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eEstimated ( Dash 8-100 data)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePolytropic compressor efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eLiterature [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eTurbine efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eLiterature [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eMechanical efficiencies\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.97 (LP), 0.98 (HP), 0.98 (PT)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eTypical\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eBleed air fraction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e3%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eCabin pressurization [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePropeller efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eIATA roadmap [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003c/table\u003e\u003c/div\u003e\u003cp\u003eSeparate values based on general PW100 family data, in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e (LP: 2.8, HP: 3.6; product ≈ 10.08, close to 12.14 with inter-stage losses) were \u003cb\u003eapproximated.\u003c/b\u003e\u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cp\u003eLP: ~2.5-3.0 (from PW100 data in Saravanamuttoo et al., Gas Turbine Theory[\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eHP: ~3.0–4.0 (centrifugal stage typical for PW120A, adjusted to match overall).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e\u003cb\u003eFuel Burn\u003c/b\u003e: \"~425 kg\" now as estimate; aligns with ~ 590 kg/h cruise rate × 0.72h effective burn time (from Airliners.net and ESFC calc).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e\u003cb\u003eOverall Deviations\u003c/b\u003e: Still \u0026lt; 2%, supporting model validity.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tab2\" border=\"1\"\u003e \u003ccaption\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValidation Results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"1\"\u003e \u003c/colgroup\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"6\"\u003e \u003c/colgroup\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eSimulated Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePublished Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eDeviation (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eNotes\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eFuel Burn (kg/flight)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e420.4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e~ 425\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eEst. from ESFC [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e] \u0026amp; mission data\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1.1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eCruise 300km, 1.2h mission\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eRange (km)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1370\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1350\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eDash 8-100 [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eFull fuel load\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eESFC (kg/kW-h)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.303\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.298\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003ePW127-E [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e1.7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eMass flow variance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eAnnual Savings (\u003cspan\u003e$\u003c/span\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e26,800\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e26,900 (midpoint)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eIATA [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eWithin range\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003c/table\u003e\u003c/div\u003e\u003cp\u003eFuel Burn Validation: Model predicts 420.4 kg/flight (two-spool). Estimated published value ~ 425 kg for Dash 8-100 (from ESFC 0.285 kg/kW-h in [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e] × 2,380 kW × 1.2h mission; cross-checked with cruise rates ~ 590 kg/h ). 1.1% déviation. ... These use Ref [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]'s ESFC as anchor, with mission assumptions for flight-specific metrics.\u003c/p\u003e"},{"header":"3. Assumptions And Limitations","content":"\u003cp\u003eIt is important to note here that our model as certain limitations. The main point is that the engine was looked at the \u0026ldquo;spool level\u0026rdquo; rather than a detailed \u0026ldquo;stage level\u0026rsquo;, where more thermodynamic nuances could be captured. Furthermore, only steady state flight was modeled, rather than the non steady state transient components ( takeoff and landing). Fuel quality was taken constant whereas in real life, the quality degrades with age.\u003c/p\u003e"},{"header":"4. Results \u0026 Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Improvement in Range and Fuelburn\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows a significant reduction from 441.4 kg to 420.4 kg with a two spool. This\u0026thinsp;~\u0026thinsp;5% improvement is expected expected due to optimized energy extraction from multiple spools and better matching of stages, [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs a result,the usable range per aircraft increases by 65 km on a full tank. Although this might seem small, over a whole fleet this figure adds up.\u003c/p\u003e \u003cp\u003eRecent turboprop optimization studies [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] support this..\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Economic Impact\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e3\u003c/span\u003e demonstrates the annual cost savings potential when adopting a two-spool configuration. With Jet-A fuel priced at \u003cspan\u003e$\u003c/span\u003e0.85/kg, the per-flight savings of \u003cspan\u003e$\u003c/span\u003e17.87 scale to ~\u003cspan\u003e$\u003c/span\u003e26,800 annually per aircraft, assuming 5 daily flights over 300 operational days. These results resonate with airline case studies in recent IATA reports, where even single-digit per cent efficiency gains lead to high ROI due to fuel cost dominance in operational budgets [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Comparison with Real-World Data\u003c/h2\u003e \u003cp\u003eOur model predicts an ESFC of 0.303 kg/kW-h, which is merely 6.3% off from the DASH 8-100\u0026rsquo;s published figure of 0.285 kg/kW-h. Such a small gap leads confidence to or initial assumption. From Fig.\u0026nbsp;4, this is a very narrow error margin, which could be fine tuned further when accounting for mechanical drag and other losses. [5.6]\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Sensitivity Analysis\u003c/h2\u003e \u003cp\u003eWhat matters Most?. We also ran several tests to see how different conditions affect the engine\u0026rsquo;s performance ( Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAltitude: Air density and drag reduce at higher flyig altitudes, improving aircraft efficiency.\u003c/p\u003e \u003cp\u003eBleed Air: It is surprisingly \u0026ldquo;expensive|\u0026ldquo; to extract bleed air for the cabin. A small increase can worsen ESFC( fuel consumption) by 4.8% - highlighting the importance of efficient pressurization.\u003c/p\u003e \u003cp\u003eMaintenance: A mere 2% drop in compressor efficiency can lead to a nearly 6% fuel spike. It is thus important to keep the compressor blades clean and well maintained.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Discussion Of The Literature","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Literature Context and Theoretical Framework\u003c/h2\u003e \u003cp\u003eThe advantages of split-spool over single spool designs have been known for some time, however the specific bench-marking has not been done. To build a solid foundation the study, Hosking et al. [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]. (covering the PW100 series), provided thermodynamic and efficiency targets for the Dash 8-100.\u003c/p\u003e \u003cp\u003eThe analytical basis provided by Saravanamuttoo et al. [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e] provide the core of our model. Their breakdown of the LP and HP spools contribution to thermal efficiency gave a framework for the cycle-based model. Schofield and Green [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e] mainly look at catastrophic failures like \"blade-offs\" in turbofan. The approach to decoupling inter spool effects helped to refine the steady-state model assumptions.\u003c/p\u003e \u003cp\u003eThe Key factors in engine architecture are Reliability and stability. De Felice and Sorrentino [\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e] look at gyroscopic stability nonlinear analysis, and this vital for any meaningful reliability projections Spataro et al. [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e] provide an explanation of the minor discrepancies—such as our 6.3% ESFC variance—often found between idealized models and actual Dash 8-100 flight data.\u003c/p\u003e \u003cp\u003eEpstein [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e] broadly highlights how changes in architectures have driventhe evolution of propulsion efficiency. The IATA Technology Roadmap [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e], identified multi-spool setups as a primary tool in achieving fuel economy for regional aviation. This industry-wide consensus confirms our findings of a ~ 5% efficiency gain over the older, single-spool variants.\u003c/p\u003e \u003cp\u003eAccording to Martin and Insausti [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e], ESFC is a reliable metric for an engine’s environmental footprint. Our own sensitivity analysis is similar. Yuksel et al. [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e] demonstrated mission-based scenarios. Their thorough evaluation of the PW127-E— from fuel mixes to various altitudes (0–9 km) and Mach numbers (0.3–0.6)—reinforces parametric modeling’s effectiveness in predicting real-world fuel costs and range. Kim et al. [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e] recommend optimization tools like genetic algorithms.\u003c/p\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusion and Practical Insights","content":"\u003cp\u003eValidation of a thermodynamic model confirmed a steady 5% fuel economy gain.Analyses clearly favour two-spool architectures for performance and operating costs. For every aircraft in the fleet it scales up to an extra 80 km of range and about \u003cspan\u003e$\u003c/span\u003e33,500 in yearly savings.\u003c/p\u003e\u003cp\u003eAlthough we made simplifying assumptions—( losses as lumped values and steady-state flight) —the model stayed within a 5–6% of official industry figures. It has yet to account for complex stage aerodynamics, transients during takeoff, and natural wear due to engine aging.\u003c/p\u003e\u003cp\u003e \u003cb\u003eCore Findings\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e \u003cstrong\u003eArchitectural Edge\u003c/strong\u003e \u003c/p\u003e\u003cp\u003eSharing power between two spools significantly optimizes thermal cycles.\u003c/p\u003e\u003cp\u003e \u003cb\u003eSensitivity Drivers: E\u003c/b\u003engineers should focus primarily on compressor health and minimizing bleed-air extraction to maximize efficiency, .\u003c/p\u003e\u003cp\u003e \u003cstrong\u003eOperational Fit\u003c/strong\u003e \u003c/p\u003e\u003cp\u003eThese benefits are seen prominently in regional, high-cycle routes profit margins vary with fuel prices.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFuture work will incorporate stage-specific loss and. Hybrid-electric configurations or geared-turbofan innovations. These could be the shift toward sustainable, \"green\" aviation.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ePLP\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eLow\u0026ndash;pressure spool power (W)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ePHP\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eHigh\u0026ndash;pressure spool power (W)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ePtp\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ePower turbine output (W)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ePacc\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAccessory power extraction (W)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003ema\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMass flow rate of air (kg/s)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003embld\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMass flow rate of bleed air (kg/s)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eCpa\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSpecific heat capacity of air at constant pressure (J/kg\u0026middot;K)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eCpg\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSpecific heat capacity of combustion gases at constant pressure (J/kg\u0026middot;K)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eT01, T02, ..., T07\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eTotal (stagnation) temperatures at various engine stations (K)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eηm,LP\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMechanical efficiency of LP spool\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eηm,HP\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMechanical efficiency of HP spool\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cb\u003eηm,PT\u003c/b\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMechanical efficiency of power turbine\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e\n\u003cp\u003e\u0026Delta; \u0026nbsp;Difference in value\u003c/p\u003e\n\u003cp\u003e\u0026delta;/ \u0026nbsp;derivative\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eE. Hosking, D. P. Kenny, R. I. McCormick, S. H. Moustapha, and A. A. Smailys, The PW100 engine: Twenty years of gas turbine technology evolution, in RTO MP-8, NATO Research and Technology Organization (1998\u0026ndash;1999).\u003c/li\u003e\n\u003cli\u003eH. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, and P. V. Straznicky, Gas Turbine Theory, 6th ed. (Pearson\u0026ndash;Prentice Hall, 2009).\u003c/li\u003e\n\u003cli\u003eJ. Schofield and N. J. Green, Mechanical loads on a turbofan engine structure at blade-off, Master\u0026rsquo;s Thesis, Lule\u0026aring; University of Technology (2009).\u003c/li\u003e\n\u003cli\u003eA. De Felice and S. Sorrentino, Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, Nonlinear Dyn. 103, 3529\u0026ndash;3555 (2021).\u003c/li\u003e\n\u003cli\u003eR. Spataro, E. G\u0026ouml;ttlich, C. Santner, and F. Heitmeir, A numerical comparison of the aerodynamic performances of a two-stage two-spool turbine facility predicted by steady and unsteady simulations, in Proc. 10th Eur. Conf. Turbomachinery Fluid Dyn. Thermodyn. (ETC10), Lappeenranta, Finland, 15\u0026ndash;19 April (2013).\u003c/li\u003e\n\u003cli\u003eA. J. Epstein, Aeropropulsion for commercial aviation in the twenty-first century, J. Propul. Power 22, 265\u0026ndash;276 (2006).\u003c/li\u003e\n\u003cli\u003eInternational Air Transport Association (IATA), Aircraft technology roadmap to 2050, IATA Technical Report (2019).\u003c/li\u003e\n\u003cli\u003eF. Vel\u0026aacute;squez-SanMart\u0026iacute;n and X. Insausti, A mathematical model for the analysis of jet engine fuel consumption during aircraft cruise, Energies 14, 3649 (2021). https://doi.org/10.3390/en14123649\u003c/li\u003e\n\u003cli\u003eO. Yuksel and H. Ayg\u0026uuml;n, Comparative performance analysis of a turboprop engine used in regional aircraft by considering design and flight conditions, Aircraft Eng. Aerosp. Technol. 97, 345\u0026ndash;355 (2025). https://doi.org/10.1108/AEAT-07-2024-0194\u003c/li\u003e\n\u003cli\u003eS. Kim, C.-R. Lee, W. Yang, and Y. Kim, Suitability of performance adaptation methods for updating the thermodynamic cycle model of a turboprop engine, Appl. Therm. Eng. 242, 122408 (2024). https://doi.org/10.1016/j.applthermaleng.2024.122408\u003c/li\u003e\n\u003cli\u003eE. Hosking, D. P. Kenny, R. I. McCormick, S. H. Moustapha, and A. A. Smailys, The PW100 engine: Twenty years of gas turbine technology evolution, in RTO MP-8, NATO Research and Technology Organization (1998\u0026ndash;1999).\u003c/li\u003e\n\u003cli\u003eH. I. H. Saravanamuttoo, G. F. C. Rogers, H. Cohen, and P. V. Straznicky, Gas Turbine Theory, 6th ed. (Pearson\u0026ndash;Prentice Hall, 2009).\u003c/li\u003e\n\u003cli\u003eJ. Schofield and N. J. Green, Mechanical loads on a turbofan engine structure at blade-off, Master\u0026rsquo;s Thesis, Lule\u0026aring; University of Technology (2009).\u003c/li\u003e\n\u003cli\u003eA. De Felice and S. Sorrentino, Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, Nonlinear Dyn. 103, 3529\u0026ndash;3555 (2021).\u003c/li\u003e\n\u003cli\u003eR. Spataro, E. G\u0026ouml;ttlich, C. Santner, and F. Heitmeir, A numerical comparison of the aerodynamic performances of a two-stage two-spool turbine facility predicted by steady and unsteady simulations, in Proc. 10th Eur. Conf. Turbomachinery Fluid Dyn. Thermodyn. (ETC10), Lappeenranta, Finland, 15\u0026ndash;19 April (2013).\u003c/li\u003e\n\u003cli\u003eA. J. Epstein, Aeropropulsion for commercial aviation in the twenty-first century, J. Propul. Power 22, 265\u0026ndash;276 (2006).\u003c/li\u003e\n\u003cli\u003eInternational Air Transport Association (IATA), Aircraft technology roadmap to 2050, IATA Technical Report (2019).\u003c/li\u003e\n\u003cli\u003eF. Vel\u0026aacute;squez-SanMart\u0026iacute;n and X. Insausti, A mathematical model for the analysis of jet engine fuel consumption during aircraft cruise, Energies 14, 3649 (2021). https://doi.org/10.3390/en14123649\u003c/li\u003e\n\u003cli\u003eO. Yuksel and H. Ayg\u0026uuml;n, Comparative performance analysis of a turboprop engine used in regional aircraft by considering design and flight conditions, Aircraft Eng. Aerosp. Technol. 97, 345\u0026ndash;355 (2025). https://doi.org/10.1108/AEAT-07-2024-0194\u003c/li\u003e\n\u003cli\u003eS. Kim, C.-R. Lee, W. Yang, and Y. Kim, Suitability of performance adaptation methods for updating the thermodynamic cycle model of a turboprop engine, Appl. Therm. Eng. 242, 122408 (2024). https://doi.org/10.1016/j.applthermaleng.2024.122408\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Applied Science Private University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Gas turbine, two spool, efficiency, fuel burn, thermodynamics, range, economy","lastPublishedDoi":"10.21203/rs.3.rs-9025558/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9025558/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA case study into the performance of two-spool turboprop engines, used the Pratt \u0026amp; Whitney PW120A to evaluate fuel efficiency, range, and economic savings. 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