Streamliner Model Scaling laws
Model scaling laws

Scanned by Nick Hein from "Design of the Aeroplane" by Darroll Stinton. c1985

While these rules were created for aircraft specific applications, they can be used to estimate the performance of a human powered vehicle by creating a model and measuring it's characteristics.

Scaling Factors

= Full scale Linear Dimensions / Model Linear Dimensions

Model Design Example for 1/5 Scale Model ( = 5)

Parameter Model Should Be: Full Scale Model
Linear Dimensions Full Scale / Span 35.8 ft 35.8/5 = 7.16 ft
Area Full Scale /2 Wing 174 sq. ft. 174/25 = 6.96 sq. ft.
Volume, Mass, Force Full Scale /3 Gross Wt. = 2645 lbs 2645/125 = 21.16 lbs
Moment Full Scale /4 Full Scale/625
Moment of Inertia Full Scale /5 Pitch:1364 slug ft.2 1364/3125 = 0.431 slug ft.2
Linear Velocity Full Scale / Max: 144 MPH 144/2.24 = 64 mph
Linear Acceleration Same as Full  Same as Full Scale
Angular Acceleration Full Scale x Full Scale x 5
Angular Velocity Full Scale x Full Scale x 2.24
Time Full Scale / Full Scale / 2.24
Work Full Scale /4 Full Scale/625
Power Full Scale /3.5 Rated: 160 hp 160 / 280 = 0.57 hp
Wing Loading Full Scale / 15.2 psf 15.2 / 5 = 3.04 psf
Power Loading Full Scale x 16.5 lbs. / hp 16.5 x 2.24 = 37 lbs
Angles Same as Full  Same as Full Scale
R.P.M. Full Scale x Rated 2740 rpm 2740 x 2.24 = 6160 rpm

Full Scale Performance from Model Test - Example for 1/5 Scale Model ( = 5)

Parameter Full Scale Should Be: Measusured Model Performance Derived Full Scale Performance
Time Model x Model x 2.24
Maximum Speed Model x 64 mph 64.2 x 2.24 = 144MPH
Max Climb Rate Model x 344 fpm 344 x 2.24 = 770 fpm
Takeoff Distance Model x 160 ft. 160 x 5 = 800 ft.
Pitch, Roll & Yaw rates Model x 50 / sec. 50 / 2.24 = 22 / sec.

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