Prototype P-36LF - Sizing Calculation and Performance Estimations

Purpose

Purpose: The purpose of this calc is to develop preliminary sizing and performance calculations for a single seat, single engine homebuilt aircraft. The P-36LF LiteFighter prototype is an approximately 55% replica of a Curtiss P-36 Hawk. These preliminary estimations are for the prototype only. Further development and refinement of the design will be incorporated into a kit version - performance calculations will be revised.

Methodology

The initial sizing of the P-36LF is performed using a comprehensive, proprietary Microsoft Excel spreadsheet ('Aircraft Design Workbook') which is heavily based on the methods described in Conceptual Aircraft Design by D. Raymer and Design of Light Aircraft by R. D. Hiscocks. Unlike a traditional aircraft design process where the aircraft's mission requirements would dictate the layout, the P-36LF layout was initially scaled from the original, with the geometry largely defined by (1) maintaining a scale appearance and (2) accommodating a reasonably sized pilot. As the design fidelity increased, the input geometry was iteratively updated to maintain acceptable performance.

The 'Aircraft Sizing Validation Workbook' consists of the following worksheets which were used to iteratively evaluated the designed, and later the as-built, aircraft parameters:

Product Specification – This worksheet is where high-level design goals (payload, speed, range) are input for use in the subsequent worksheets. Certain 'fixed' inputs, such as pilot, payload, and number of engines are used throughout the workbook whereas 'flexible' inputs such as wing loading and range are only estimates used for initial sizing. Note the flexible values are carried from the preliminary sizing and may not reflect the as-built condition.

Summary Sheet – This worksheet contains summarized dimensional and performance estimations for the as-built design.

Powerplant – This worksheet contains engine and propeller data that is used throughout the workbook. Data for alternate engine options is also contained in this sheet but is not used in the workbook.

Fuselage & Cabin – This worksheet provides basic dimensions for the fuselage for use in aerodynamic calculations for drag and stability.

Main Wing, Horizontal Stabilizer, and Vertical Stabilizer Layouts – These worksheets are used to input the geometry of each flying surface and control surface, which is then used to calculate several geometric coefficients for use throughout the workbook.

Weight and Balance – This worksheet calculates the load envelope based on the measured empty weight and CG from the as-built prototype.

Surface Data Calculated – This worksheet contains aerodynamic coefficient data for use throughout the workbook. Data input comes primarily from XLFR5 simulations.

Performance Estimation – This worksheet calculates a thrust-drag balance at various altitudes and airspeeds to determine climb rate and level flight performance.

Longitudinal Stability – The aircrafts stick free and stick fixed neutral points and static margin are calculated using the methods from the aforementioned material. A trim plot is used to find the optimal horizontal stabilizer angle.

Balance Loads – This worksheet calculates the tail force necessary to generate the design maneuvering loads.

 Spin Recovery – This worksheet calculates the tail area that is assumed to be not blanked by the horizontal stabilizer in a spin and compares it to empirical factors to determine if spin recovery is possible.

Drag Buildup – This worksheet estimates several drag coefficients which are used to determine overall aircraft performance.

 Load Envelope – The V-n diagram (load envelope) is developed, including gust loads.

Reference Data Worksheets – Several worksheets contain reference data from various sources.

Results

The basic sizing and capabilities of the P-36LF is identified below. Calculation was rerun in 2021 with actual weights from the (nearly) completed aircraft. The results of the iterative sizing and weight estimation is shown below representing the as-built condition. Due to the increase in empty weight, the gross weight increased from 1036 to 1232 lbs. Actual fuel tank volume is slightly below the estimated value, which results in 12 lbf (2 gal) less fuel capacity. Note that the gross weight increase was driven by the desire to maintain the same payload, a lighter gross weight can be assumed, however pilot weight will be limited and likely wouldn’t accommodate a 95th percentile male.

Performance results are as-expected for an aircraft of this size, power, and design. Performance is decreased slightly, as expected, from the preliminary estimations. The max level flight speed and cruise speed as shown are unchanged; however, the stall speed increased to 54 knots assuming a gross weight plus balance load of 1232 lbf. The stall speed does not meet the LSA stall speed requirement of 45 knots, but does meet the FAR Part 23 single engine requirement of 61 knots. Climb performance is decreased but is still reasonable for an airplane in this category, especially given the conservatism due to uncertainty in both the thrust, drag, and weight estimations. Although the service ceiling is not explicitly calculated, performance at 12,500 feet (the maximum altitude before oxygen is required) is significantly diminished, therefore 12,500 feet will be designated service ceiling.

The load limit has been reduced to +3.8g (normal category) in order to maintain margin to the structural design due to the increased gross weight. This results in a roughly 5 knot decrease in maneuvering speed to between 99-102 knots, accounting for margin of error in lift coefficient calculation.

Conclusion

While performance is expected to be somewhat reduced from the initial design parameters for the concept aircraft, flight characteristics are well within safe operating parameters and it is recommended to proceed with flight testing. Validation of many of the estimated coefficients used in the calculated numbers will be required via extensive flight testing. Actual performance is likely to be different than shown below and will be used to inform the calculation package and redesign of the kit version of the airframe. This is a proof of concept and engineering prototype. The future version of this design will have higher performance and capabilities.