Conan,
If you are familiar with differential calculus, then the above explanation will have convinced you that profile drag is equal to induced drag at Vmd. But if you are not familiar with differential calculus, then you will be none the wiser. If this is the case, it might help to start with a less mathematical approach.
You are probably happy with the facts that:
1. Profile drag increases as airspeed increases.
2. Induced drag decreases as airspeed increases.
3. Total drag is equal to Profile Drag + Induced Drag.
4. The total drag curve looks like a bucket shape.
Looking at the total drag curve we can see that it has a steep downward slope at the low speed end, a steep upward slope at the high speed end, and is flat where its value is lowest at Vmd, somewhere between the two ends. The important thing to note is that total drag is minimum at the speed at which the slope of the curve is zero.
Total drag = profile drag + induced drag, so the slope of the total drag curve is the sum of the slopes of the profile drag and the induced drag curves.
The total drag curve is zero when the upward slope of the profile drag curve is exactly equal to the downward slope of the induced drag curve. This occurs at the bottom of the total drag curve, where the speed is Vmd.
In differential calculus the process of differentiation provides a means of finding the slopes of these curves.
In BEagle’s explanation:
The first line states that Total Drag = Profile Drag + Induced Drag
The second and third lines derive the conditions in which the slope of the total drag curve is zero. Remember this is at Vmd at the bottom of the total drag curve
The subsequent lines develop this to show that at Vmd Profile Drag is equal to Induced Drag.
Last edited by Keith.Williams.; 9th May 2010 at 16:21.
Reason: Tooping Errot