# Lift-dependent drag estimation

1. Dec 25, 2013

### NTW

I'm no engineer, but just a pilot trying to estimate the drag of my small two-place airplane from the relevant formulae.

My plane is quite draggy, and from comparison with other aircraft data, I have taken Cd,0 as 0.043. Apart from this, I calculate the induced drag at a given speed from the lift, equal to the weight in S&L flight, air density, wing area, aspect ratio and applicable Oswald number (I've taken 0.73). So far, so good, but I have doubts concerning the lift-dependent drag. In a solved problem in Anderson's Aircraft Performance and Design, the author estimates (for a Gulfstream) that lift-dependent drag as 1/3 of the induced drag.

Should I take that figure for my calculations? I don't feel sure, since 1/3 is a lot...

2. Dec 25, 2013

### rcgldr

I had the impression that induced drag and lift dependent drag mean essentially the same thing. In an ideal case, at the best lift to drag ratio (best glide ratio) which occurs at a specifc speed, and the induced drag is 1/2 the total drag. However most powered aircraft travel at "cruise speed" which is well above the speed associated with best lift to drag ratio, so most of the drag is parasitic / profile drag.

3. Dec 25, 2013

### NTW

Well, yes, but -in general- the induced drag coefficient calculated by Cl^2/pi*e*AR corresponds only to the lift-vortex drag. Since the profile drag varies with the attitude of the plane, there is a complementary profile drag that is the lift-induced drag, which can be estimated as a fraction of the latter. My query is about the magnitude of that fraction...

4. Jan 7, 2014

### rcgldr

There are variations in the definition of induced drag, but the concept is easiest to visualize using an ideal wing that from the wing's frame of reference, diverts a relative flow (the mass of the affected air per unit time) by some average angle downwards without changing the speed of the air, so no change in energy from the wings frame of reference. (From the air's frame of reference energy is added to the air, resulting in downwards and some forwards flow). The horizontal component of velocity of the flow is decreased by 1 - cos(angle of deflection). Assuming lift equals weight, then you can used the idealized formula for induced drag based on the average angle of deflection:

induced drag = lift (1 - cos(θ)) / sin(θ)

The issue then is how to determine the average angle of deflection. I don't know if there is a simplified approximation for this based on an aircraft and it's wing parameters.

However, getting back to my previous post, if the best glide ratio and corresponding speed are known, then assume that 1/2 the drag is induced drag. Lift always equals weight, so the two components of drag equal 1/2 the weight x drag / lift (drag/lift = 1 / (glide ratio)). Then for the best glide ratio parameters, let V0 = speed of best glide ratio, Di0 = induced drag at best glide ratio and Dp0 = parasitic drag at best glide ratio. Then for approximation, Di ~= Di0 (V0/V)^2, and Dp ~= Dp0 (V/V0)^2, and Di/Dp ~= (V0/V)^4.

Last edited: Jan 7, 2014