# Achieving dynamic similitude by sacrificing geometric similitude?

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.

• 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... – Solar Mike Apr 2 '20 at 4:33
• 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. – Phil Sweet Jan 15 at 1:04

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.