Imperial 2015 Application Question

[XJS]

Hi all! I have been accepted by a university and have been given the second round interview question.

However, I am pretty stumped as to how to answer it. Here's the question:

Please answer the following question. Your answer should be handwritten on no more than three (3) sides of A4 paper. Note this is an open-ended question: there is no ‘right answer’! You are free to make any assumption you feel is necessary. Your existing mathematics and physics knowledge will be sufficient to answer this question, but you may need to apply your knowledge in an unfamiliar way.
If a sheet of paper were dropped from a helicopter hovering at a height of 1000 m, (i) with what force would it hit the ground? (ii) how long would it take to reach the ground? (iii) would your answer be different if the helicopter were moving?


For this question I want to find out:
1) Downwards force of paper
2) Downdraft of helicopter (caused by lift) onto the paper)
3) Reynolds number of air column from ground to helicopter to find out if airflow is turbulent or laminar (I'm not even sure if airflow has turbulent or laminar properties. I only learned that for fluid within pipes)
4) How do I calculate reynolds number if I don't know the cross-sectional velocity?
5) Upwards resistance of air (Terminal velocity. I really don't know how to calculate this part)
6) At which point will the paper reach terminal velocity (so I know the time and the distance), then subtract that distance from 1km to find out the remaining time it takes for the paper to hit the ground.

Point 6 continued) Essentially, I will need t [tv] (time to to terminal velocity) + t [tvg] (time it takes to reach ground after achieving terminal velocity)
Anyone have any ideas? Thank you !

 

[CWatters]

1000m is quite high and sheets of paper aren't the most aero dynamic of objects. Try dropping some sheets. Personally I don't think I would use any maths at all to answer this question.

Perhaps start with...

You are free to make any assumption you feel is necessary.

 

[Robin04]

I would assume that the paper is rigid and always horizontal. Mark a zone where the downdraft of the rotors is not negligable. Describe how will this zone effect the movement of the paper. After leaving this zone what will be the constant speed the paper is descending with (weight = drag). If the helicopter is moving the drag will have a different direction. You can also assume that the paper has thickness.

 

[CWatters]

I wouldn't assume it stays rigid and horizontal. Is that likely? I think I'd assume it swoops about all over the place making it impossible to predict exactly how long it will take to fall or how hard it will eventually land. That doesn't mean you have nothing to say about the motion in the various zones. Have you considered doing an experiment to estimate the terminal velocity?

 

[Robin04]

I wouldn't assume it stays rigid and horizontal. Is that likely?

Yes, you are absolutely right. My assumption wouldn't reflect the reality. The reason I would have assumed it to be rigid and horizontal is that in that case I can do more calculus on the happenings. If I see well, this exercise measures your skill of problem solving. The more problem you make for yourself and the more problem you solve, the more precise picture you show about your skills. Unfortunetaly I'm not an aerodynamics expert, that can also be a reason why I would assume it to be rigid and horizontal. :)

 

[XJS]

I'm having quite the problem here.

I have found out that according to FAA, minimum altitude for flying is 1000 ft (about 300m), so I am going to assume that the zone at which downdraft affects the paper is 300m.

What I need to find out in this 300m is
1) does the paper reach terminal velocity?
- In the terminal velocity formula, I am required to use mass and drag coefficient.
- I don't know the drag coefficient of paper and without drag force, I cannot find out the drag coefficient. Anyone have any ideas?
Drag formula: F = 0.5 CρAV^2
A = Reference area, m2.
C = Drag coefficient
F = Drag force, N.
V = Velocity, m/s.
ρ = Density of fluid (liquid or gas), kg/m3.

2) In the terminal velocity formula, I am required to use mass.

- In this formula, does the mass refer to only the paper? Does it include the mass of the helicopter as well?
(Because the total downward force is weight of paper + weight of helicopter due to lift. ie. downwash)

 

[CWatters]

I believe you are over thinking the problem but if that's the way you want to go..

does the paper reach terminal velocity?

Have you seen leaves falling? They reach terminal velocity in a few feet. Your paper is falling 3000ft. I think it's fair to assume it will reach terminal velocity! (If you assume it's floating down horizontally).

The paper will probably exceed terminal velocity immediately under the helicopter. Google quickly found..

http://www.copters.com/aero/hovering.html

Air velocity under the helicopter may reach 60 to 100 knots, depending on the size of the rotor and the gross weight of the helicopter.

I don't know the drag coefficient of paper and without drag force, I cannot find out the drag coefficient. Anyone have any ideas?

Why not just drop a piece of paper out of a window and estimate the terminal velocity that way :-) If you really want to you could use that result and run the numbers backwards to calculate the Cd. Have you tried Googling the Cd of a flat plate.

https://www.google.co.uk/?gws_rd=ssl#q=drag+coefficient+square+plate

At one interview I went to they asked questions that you could not possibly know the answer to. They just wanted to see what you would do.. Would you panic and get all flustered? Would you try and answer it (and fail because it's impossible)? or tell them you don't know but knew where to look to find the answer?

 

[XJS]

Thank you for your reply!

Apologies to my first post. It isn't really an interview question. They sent me this question and I have a week to reply (due 2nd March). They just called it an "overseas interview"

It was quite informative. Am I really overthinking this? I just don't want to fail, that's all. Just want to make sure my answer is correct and I'm not sure what kind of assumptions I can make that will seem like I'm trying to make the question too easy for myself.

i.e, Is it safe to just assume the air velocity under the helicopter is at 100 knots?

 

[Andrei Badea]

Thank you for your reply!

It was quite informative. Am I really overthinking this? I just don't want to fail, that's all. Just want to make sure my answer is correct and I'm not sure what kind of assumptions I can make that will seem like I'm trying to make the question too easy for myself.

i.e, Is it safe to just assume the air velocity under the helicopter is at 100 knots?

I think you're overthinking it. Anyone can solve a physics problem, especially if they applied to Imperial. It's an overseas interview, and they already know you have the physics skills from your application.

They want to see your train of thought, the way you can answer the question in an original way. Don't forget that they wrote this:
"Note this is an open-ended question: there is no ‘right answer’!" and "Your existing mathematics and physics knowledge will be sufficient to answer this question, but you may need to apply your knowledge in an unfamiliar way."

All they want to see is how you think, not values themselves or calculations. After all, they want to know you, as that's what an interview is for. Try to be original.

 

[Jerome-Dan]

I got exactly the same question for my application last year, I'm from france and I got in! Good luck with it ;)