For readers who do not like maths and like calculus even less, we can use the diagram in post number 7 to see why increasing drag does not necessarily cause an increase in power required, and also why Vmp is not the same as Vmd. (This method is just the poor man’s calculus)
Hopefully we can all agree that Power Required = Drag x TAS.
Looking at the diagram in post 7 we can see that TAS is increasing left to right along the horizontal axis and Drag is increasing from bottom to top on the vertical axis. The area within these two axes is marked off in squares.
Power required = Drag x TAS. But at any point on the Drag curve, Drag x TAS is also the area beneath the curve between the origin and that point on the drag curve. So we can calculate the power required at any point on the drag curve by counting the squares.
So, for example at Vmd (at the bottom of the Drag curve) we have an area made up of about 7 squares along the TAS axis and 3 squares up the Drag axis. This gives an area of 7 x 3 = 21 squares. This means that the power required at Vmd is proportional to an area of 21 squares.
Vmp is the speed at which the power required is the least. So Vmp must be the same speed as a point on the drag curve at which the area below the drag curve is the least.
If we count 5 squares along the TAS axis, we can see that there are about 3.6 squares up the Drag axis, so we have an area of 5 x 3.6 = 18 squares. This is less than the 21 squares at Vmd, which means that the power required at this new speed is less than at Vmd. So we have moved closer to Vmp.
If we count 4 squares along the TAS axis, we can see that there are about 5 squares up the Drag axis, so we have an area of 4 x 5 = 20 squares. This is more than the more than 18, so we have moved beyond Vmp. So Vmp is somewhere between 4 squares and 5 squares along the TAS axis.
If we count 4.75 squares along the TAS axis, we can see that there are about 3.75 squares up the Drag axis, so we have an area of 4.75 x 3.75 = 17.8 squares. This is lower than the previous value, so we have moved closer to Vmp.
We could keep on repeating this process until we reached a good approximation for Vmp. Or if we wanted to we could short-cut this process by drawing a straight line that started at the origin and crossed the drag curve at 90 degrees.
Last edited by keith williams; 24th Mar 2014 at 13:04.