Lift and drag equations for RC planes

I'm going to keep these explanations to the main points only and then at the end I'll give a link or two for further reading providing I can find some good links...

These equations are on the same page for a reason. Firstly they will be at the core of our understanding and (simple) modelling of flight, and secondly, they are both very similar. Here they are...

1. The Lift Equation:

2. The Drag Equation:

Before I go further, lets define the terms:

L. lift, measured in Newtons (N)

D. drag, measured in Newtons (N)

ρ. (Greek letter 'rho') air density, measured in kgm^-3

V. velocity, measured in ms^-2

S. area, measured in m² (Note that this is taken as wing surface area as viewed from above)

C_D ad C_L. Coefficients of drag and lift, no units.

You'll notice that both equations are fairly similar - on the right hand side both equations have the first four terms the same. This is because both of these equations are describing effects of interaction of a body with air: The first three terms are 'dynamic pressure' and the fourth term is the surface area being acted on.

The final terms are those that give the equation a meaningful answer. These are the coefficient of lift and the coefficient of drag. These can be estimated from known figures on similar bodies or they can be determined by wind tunnel testing. (For our purposes in this project we'll use estimates from existing data and we'll always round them up/down against us.)

Note about C_L and C_D

Bear in mind ANY other factor you can think of that would affect lift is taken into consideration with the lift coefficient and likewise for the drag. So, lift coefficient will vary with angle of attack for example, and drag coefficient will vary with angle of attack too (induced drag).

Using the Lift and Drag equations

Although they are essentially simple equations we can get a lot of useful information from them.

For level flight for instance we know that lift must equal weight.

i.e. W = L = [equation above]

Now, with respect to the above lift equation, air density can be known for any altitude, surface area is known, and the lift coefficient can be known for a certain angle of attack (or a range of angle of attacks, which gives a range of C_L).

Now we can simply rearrange the formula to find the only unknown: V, the required speed to balance the equation and hence the required speed for level flight.

i.e.

Quick recap. What we've done is find out what speed a plane needs to fly at given a certain weight, air density and lift coefficient.

Now lets work out the drag. This is simply back to the drag equation:

We fill this in using the speed we just worked out, the same air density and area and the estimated value of drag coefficient. (I suggest the best you might be able to do is search online to find out what drag coefficient you should use for your model type and covering.)

As some of you will already be thinking, in finding out the drag we have also found out required thrust for constant speed flight since drag is equal to thrust in that scenario.

I'll take it further on another page soon.

Paul


	Lift and drag equations for RC planes I'm going to keep these explanations to the main points only and then at the end I'll give a link or two for further reading providing I can find some good links... These equations are on the same page for a reason. Firstly they will be at the core of our understanding and (simple) modelling of flight, and secondly, they are both very similar. Here they are... 1. The Lift Equation: 2. The Drag Equation: Before I go further, lets define the terms: L. lift, measured in Newtons (N) D. drag, measured in Newtons (N) ρ. (Greek letter 'rho') air density, measured in kgm^-3 V. velocity, measured in ms^-2 S. area, measured in m² (Note that this is taken as wing surface area as viewed from above) C_D ad C_L. Coefficients of drag and lift, no units. You'll notice that both equations are fairly similar - on the right hand side both equations have the first four terms the same. This is because both of these equations are describing effects of interaction of a body with air: The first three terms are 'dynamic pressure' and the fourth term is the surface area being acted on. The final terms are those that give the equation a meaningful answer. These are the coefficient of lift and the coefficient of drag. These can be estimated from known figures on similar bodies or they can be determined by wind tunnel testing. (For our purposes in this project we'll use estimates from existing data and we'll always round them up/down against us.) Note about C_L and C_D Bear in mind ANY other factor you can think of that would affect lift is taken into consideration with the lift coefficient and likewise for the drag. So, lift coefficient will vary with angle of attack for example, and drag coefficient will vary with angle of attack too (induced drag). Using the Lift and Drag equations Although they are essentially simple equations we can get a lot of useful information from them. For level flight for instance we know that lift must equal weight. i.e. W = L = [equation above] Now, with respect to the above lift equation, air density can be known for any altitude, surface area is known, and the lift coefficient can be known for a certain angle of attack (or a range of angle of attacks, which gives a range of C_L). Now we can simply rearrange the formula to find the only unknown: V, the required speed to balance the equation and hence the required speed for level flight. i.e. Quick recap. What we've done is find out what speed a plane needs to fly at given a certain weight, air density and lift coefficient. Now lets work out the drag. This is simply back to the drag equation: We fill this in using the speed we just worked out, the same air density and area and the estimated value of drag coefficient. (I suggest the best you might be able to do is search online to find out what drag coefficient you should use for your model type and covering.) As some of you will already be thinking, in finding out the drag we have also found out required thrust for constant speed flight since drag is equal to thrust in that scenario. I'll take it further on another page soon. Paul