My prof is the type who makes up his own questions (rather than pulling them from textbooks). This is his latest work... Anyone got any ideas on how to solve this? He assures me that you don't need velocity or chord or additional info (like Mach numbers) to figure it out and I keep ending up with 3 unknowns with only 1 or 2 equations! Here's the question:

High-performance gliders have very large aspect ratios in order to soar efficiently (for reasons we will discuss later in the course). A 1:30 scale glider model with an aspect ratio of AR=30 is tested in a water tunnel, and found to have a lift coefficient of CL=0.8 at a Reynolds number of Re=2.0*10^6. Based on this result, what is the maximum mass of a full-scale glider, operating in air at the same Reynolds number, that can maintain level flight? Give your answer in kg.

Acceleration due to gravity: g=9.81 m/s^2

For water: ρ=1000 kg/m3 and μ=1.0*10^-5 kg/ms

For air: ρ=1.2 kg/m3 and μ=1.9*10^-5 kg/ms

  • $\begingroup$ Hint: it's a trick question. None of the detailed information has any relevance to the answer. $\endgroup$ – alephzero Jan 18 '20 at 15:05
  • $\begingroup$ @alephzero Gravity certainly does! $\endgroup$ – Phil Sweet Jan 18 '20 at 15:07
  • $\begingroup$ You do need some additional info, such as some sizing info or model measured load. $\endgroup$ – Phil Sweet Jan 18 '20 at 15:12
  • $\begingroup$ How is that possible? I figure that out boils down to the lift equation but velocity and area are both defined as ratios and I can't figure out how to make done for one or the other (along with mass) or how to relate them in a way that helps to work toward the solution. I've spent about 5 hours on this question and I keep going in circles. $\endgroup$ – Nalorin Jan 18 '20 at 19:43
  • $\begingroup$ figure out how to solve* for one or the other... (sorry, I responded on my phone previously). @alephzero that's not really a hint - that's basically saying "yes, you can solve it using the information in the question." Can you please provide some feedback that's a little more useful? $\endgroup$ – Nalorin Jan 18 '20 at 20:25

I discovered the solution method through more banging head against a wall:

You have to do a double-substitution of velocity and chord, together, and you only need to focus on the prototype.

Solve Reynolds equation for uc (uc = Re*(mu)/(rho)) Use Aspect ratio to find area in terms of chord only (S = c^2 * (AR)) Plug area into lift force equation Rearrange to get (uc)^2 in the equation and solve using values for (rho), (uc), C_L, and (AR).

  • $\begingroup$ Plus 1 for the effort well done $\endgroup$ – Solar Mike Jan 19 '20 at 14:46

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