Fluid, Thanks so much for posting that - very useful!
Ideasrule - I think Fluid is right, it is cos of the angle. The horizontal distance Fluid gives is the adjacent, the vertical distance is the opposite. theta is arctan opp/adj. The increase in speed along the hyp is given by cos...
I'm pretty certain the speeds DON'T have to match, Phrak. Imagine a scenario where the 2nd plane had no drag (I agree, very unrealistic!). then all of its PE could be converted to KE, and the velocity gain would be huge v=sqrt(2gh2), or sqrt(2x9.8x50) if we work in SI units, or 30 or so metres...
I think that's probably right, Phrak. I just don't know how to do it.
I think you can ignore the levelling out part, assume that the plane continues to dive until the point where it either overtakes the faster aircraft, or runs out of its height advantage. those are your boundary conditions.
QueenOfBabes - you're not the only one!
djeitnstine - I don't think you need to consider an increase in cross sectional area in the vertical plane. Remember the plane will be moving such that the cross sectional area relative to the airflow will remain constant - the velocity vector will...
Guys, I've just looked up the Brachistochrone problem, and I think this problem is a bit different. The Brachistochrone problem doesn't consider aerodynamic drag, which is going to be the dominant speed limiting factor here.
Remember, we are talking about aircraft which are initially at an...
Thanks for the replies guys, I didn't expect such enthusiastic responses so quickly!
Berkeman - With regard to the question of whether the top plane overtakes the slower one, this is a real world situation that occurred in a handicapped aircraft race last week. The question I'm really...
Hi, I don't know how hard this problem really is, I've tried setting up a differential equation and get garbage answers. Can anyone help me?
Imagine two identical aircraft with identical drag, wing area and thrust but different payloads, such that one has a max straight and level speed of...