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Max Range and Max Endurance speeds?
Is it possible to determine the max range speed, knowing only the max endurance speed given this model:
D(v) = av^2 + (b/v^2)
where minimizing D(v) gives best endurance and minimizing D(v)/v gives best range.
1 Answer
- AslanLv 61 decade agoFavorite Answer
D = av^2 + bv^-2
D' = 2av + -2bv^-3
D" = 2a + 6bv^-4
stationary min/max points are where D' = 0
2av -2bv^-3 = 0
2av = 2bv^-3
av = bv^-3
v/v^-3 = a/b
v^4 = a/b
so a stationary point for any value of a where b =/= 0
placing this value into D" to determin the type of stationary point
D" = 2a + 6b^2/a
so seeing as we need a minimum point then we need D">0
therefore 2a + 6b^2/a >0
the 6b^2 will always be >=0
for a+0 we get an undefined answer
so we can say that for a>0 we get a D">0 and the minimum point we are looking for in any value of b
