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The goal is to scale up a general aviation aircraft by 15%. Dynamic similitude is the primary goal.

I have reviewed research on scaling aircraft models but it seems most of it is focused on creating geometric scaled models and using various methods to interpret the data and make it applicable to the full scale aircraft.

I am seeking advice for how to create a scaled aircraft where the primary objective is dynamic similitude, with no regard given to geometric similitude.

The aim once again is to scale up an existing aircraft design while keeping the flight characteristics as similar as possible.

Thank you for your time.

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  • $\begingroup$ Yes, you play off the ones you want against the ones you don’t - one method was to run flow tests in water as density is a factor of 1000 more... $\endgroup$
    – Solar Mike
    Apr 2, 2020 at 4:33
  • $\begingroup$ Please state exactly what dynamic similitude entails. What are the stability derivatives you are considering, and is your dynamic model linear, partially nonlinear, or fully nonlinear? Are you only concerned with stability modes and their eigenvalues, or are you looking at the entire aircraft's control ensemble. Are you using software for the dynamic modeling, or hand cranking the stuff. $\endgroup$
    – Phil Sweet
    Jan 15, 2021 at 1:04

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This is actually a bit more complicated than first appears.

Just one step is to maintain the Reynolds number

$\text{Re} = \frac{v\cdot l\cdot\rho}{\mu}$

v = flow speed

l = characteristic length along the flow path, like wing chord

ρ = fluid density

μ = dynamic viscosity of the fluid

and that means to get the same Reynolds number on a wing scaled down by four you need 4 times faster wind.

In real wind tunnels, they know this means supersonic speeds. So they run the test with a slower wind but with correction equations many times built into the hook's strain digitizer.

Basically because of nonlinear relation between air inertial properties and its dynamic viscosity a wing or a plane can not be modeled linearly.

The second step is the Mach ratio, relative speed of wing to speed of sound.

One way to make the scale behave similarly is to increase the air pressure hence density by reverse off scaling factor.

There are some other factors to watch for.

This link may help you as a starting point. Scaling of planes

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  • $\begingroup$ I followed your suggested links and read most of the NASA article on scaled models. I still am struggling to make the connection with how to scale up a design. The literature is rife with examples of using a geometrically scaled much smaller model and interpreting the data to apply to the larger model. But in terms of how to apply this increasing a plane's size/gross weight by 15% and maintaining similar flight characteristics is beyond me. Do you have any suggestions on how I can bridge this gap in my understanding? Thanks! $\endgroup$
    – MedicalFlyer
    Apr 13, 2020 at 17:48
  • $\begingroup$ The simple answer is no. the wind tunnel plane models are scaled-down models with all the wings sections and articulation exactly the same. They just know how to consistently correct for lif and drag and other aerodynamic features. but if you change the profile of a wing to give you the same lift properties at a certain speed, its behavior at other speeds are not correlated. you cant predict lif, stall speed, drag for other speeds. $\endgroup$
    – kamran
    Apr 14, 2020 at 18:18
  • $\begingroup$ My apologies for spelling errors used my phone. read lift for lif. $\endgroup$
    – kamran
    Apr 14, 2020 at 18:25

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