1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Dimensional analysis check

  1. Aug 12, 2013 #1
    1. The problem statement, all variables and given/known data

    An flying object of mass M experiences a lift force and a drag force dependent on the it's velocity:

    [tex] F_{l} \propto Wv^{2} [/tex]
    [tex] F_{d} \propto Av^{2} [/tex]

    Where W and A are wing surface area and "cross-sectional" area.

    To sustain flight the object must fly at a minimum velocity which scales as [itex]M^{k} [/itex] where k is a constant.

    What is k?

    2. Relevant equations

    For the object to remain in flight it must produce a lift force equal or greater than it's weight i.e.

    [tex] Mg = F_{l(min)} \propto Wv^{2} [/tex]

    3. The attempt at a solution

    I have found an answer but I'm not too happy with how I got there. Basically, I subbed the scaling factor for minimum velocity into the above equation:

    [tex] Mg \propto W(M^{k})^{2} \propto WM^{2k} [/tex]

    As the left side only has mass to the power 1 and the right has mass to the power 2k we can get:

    [tex] 2k=1 [/tex]

    So k = 1/2 or [itex]v_{l(min)} \propto \sqrt{M} [/itex].

    This results makes some sense to me physically, but I'm not happy with my approach as it seems a bit simplistic.
    Last edited by a moderator: Aug 12, 2013
  2. jcsd
  3. Aug 12, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Seems fine to me. If you increase the mass by a factor of ##2## you need to increase the velocity by a factor of ##\sqrt{2}##, all else being fixed. What seems simplistic about it to you?
  4. Aug 13, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Maybe you are supposed to assume that the object is to be scaled linearly at constant density. Thus W and A will also change.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted