Drag coefficeant rearranging equations problem

• Jan 16th 2010, 10:13 AM
tomarsawrous
Drag coefficeant rearranging equations problem
Hi all, thanks for you time...

I'm trying to work out how the answer for this problem is obtained:

Q. The drag coefficient for an aircraft is reduced by streamlining.

For the same power output and frontal area by what percentage is the flight speed increased if the drag coefficient is reduced by 18%.

A. The expression of power through drag P=DxV and the power remains the same so that P1 = P2 (i.e D1 x V1 = D2 x V2)

Now replacing D1 and D2 with the formula for drag and cancelling like terms I am left with (coefficient of drag) C1 x V1^3 = C2 x V2^3

This is where I get stuck, C2 is equal to 0.72 x C1 (-18%) which obviously is input into the above equation but I cannot obtain the answer, which I believe to around a 7% speed increase.

Thankyou

Tom
• Jan 16th 2010, 10:34 AM
TKHunny
That wasn't bad. It's always irritating to get the hard part and stumble on the simple stuff you know already. Good work, though. It better than the other way around. Reviewing always gets in the way of advancement.

If C1 * V1^3 = C2 * V2^3
And If C2 = 0.72* C1
This gives: C1 * V1^3 = (0.72*C1) * V2^3

Solving for V2 in terms of V1 gives: $\displaystyle V2 = \sqrt[3]{\frac{V1^{3}}{0.72}} = \frac{V1}{\sqrt[3]{0.72}} = \frac{V1}{0.896281} = 1.115722 \cdot V1$

Can the question now be answered?