Re: Can you help me design a helicopter propelled by a rubberband?

Dear Kate,

	This is a very complex problem from an engineering/design 
standpoint, but I can see why your teacher wants to do this, as helicopters 
are cool flying machines.  Complete understanding of the physics of 
helicopter flight is likely much beyond your scope, so I will try to limit 
my explanations to the parts that are relevant to your vertical only 
flight.  I will also give you some design recommendations, but I won't 
build the whole thing for you!  Many of the terms I will use can be found 
at the following website:

http://www.copters.com/helo_aero.ht
ml
and if you have other questions, the site owner (Paul Cantrell,  
paul@copters.com) will likely be a great resource.  Some of the concepts 
will 
probably be over your head but many you will be able to understand and he 
has 
great illustrations of what is going on, so I recommend looking at the 
sight 
thoroughly.

	One of the problems with the earliest helicopter designs was the 
fact that once they got off the ground, the entire helicopter body began to 
spin the opposite way of the rotors.  This comes from Newton's third law of 
motion, "to every action there is an equal and opposite reaction" (that is 
the paraphrased version).  If you are spinning the rotors and they have 
both inertial resistance and wind resistance, you need to apply a torque to 
the rotors for them to spin.  In order to not spin the body, an equal and 
opposite torque to the body needs to be applied.  An experiment to test 
this would be to stand on one of those rotating platforms (you teacher may 
have one) and try to spin (like helicopters blades) a heavy umbrella or 
something similar above your head.  See if you can stay motionless on the 
platform and start and stop the umbrella.

	There are two methods for dealing with this spin.  One is the tail 
rotor that nearly all helicopters you see have.  The tail rotor serves two 
purposes, one to steer the aircraft and the other is to counteract the spin 
from the main rotors.  The other method to counteract the spin is to have 2 
main rotors that spin in opposite directions.  (One rotor is on top of the 
other and have separate drive shafts, usually a solid one inside for the 
top rotor and a hollow one outside for the bottom rotor).  This is a much 
rarer configuration but some helicopters do have them.  One other method 
that would work for you, but not in real life, is to put a big fin on the 
tail and use wind resistance to slow down the spin.  This may seem like a 
pain in the rear to deal with, but I can guarantee that those students who 
do not deal with the spin issue will have troubles winning, as the spinning 
saps the power from the rubber band.  (If the inertia and wind resistance 
of the helicopter body is nearly the same as the rotors, it is conceivable 
that once the helicopter rises from the ground, it will hover in place as 
the body will begin to spin as fast and in the opposite direction of the 
rotors, meaning no power goes toward lift).

	In order to get lift, there are two ways to get it.  One is airfoil 
lift.  If the rotor blade has a cross-section shaped like an airplane wing, 
there is some lift due to the pressure differences.  (An airfoil is flat on 
the bottom and rounded on top.  As air passes over and under the airfoil, 
the air on top has to travel further than the air on the bottom to reach 
the same spot they were in before.  Since the air has to travel further on 
the top, its speed is greater, therefore its pressure is less compared to 
the air on the bottom of the wing.  Since there is greater pressure below 
and less above, this is where your lift comes from.  Ask you teacher if you 
are confused).  The other method of lift comes from the angle of attack of 
the rotors.  If you turn the rotor blades at an angle with the front 
(leading edge) of the blades above the back edge of the blades (see angle 
of attack section in the website I gave you) you push more air under the 
blades than over, which also increases pressure below the blades in 
relation to the pressure above the blades.  This gives greater lift.  The 
control in a helicopter for the angle of attack is called the collective.  
There is likely an ideal angle of attack for maximum lift, but it likely 
depends on how much torque your engine (in this case the rubber band) can 
produce.  If you angle is too great, the engine can't spin the rotor fast 
enough for lift off.  I would recommend, if you are allowed, just buying a 
rotor from a hobby store since airfoils are complex and not easy to build. 

 If you do have to make them, just use something flat and narrow and vary 
your angle of attack to get your lift.  You might need to put an outer ring 
on the blades for support the way some RC copters do since the blades will 
see high loads.  (Remember, the blades are where all your lift comes from). 
 The ideal angle of lift will come from experiment.  If you can't change 
it, chose something small like 10°-15°.  This is likely a good question for 
Paul Cantrell.  Also, the length and area is important.  The greater the 
length and the area of the blade will increase lift, but too long and big 
and the rotors may break.  Also, the rubber band needs to be able to make 
them go fast enough for lift off.  (Greater inertia and resistance that the 
rubber band needs to overcome when the rotor becomes bigger).  The math is 
a little tricky to figure this out on paper, experimentation may be a 
better approach to find the best rotor size.  Probably whatever you can 
just fit inside the 50cm box would be ideal!

	The last issue is balance.  Since you can't steer the helicopter, 
it needs to be very well balanced, both front to back and side to side in 
relation to the center of the rotor.  If it is not, as the helicopter rises 
it will tip, and the rotors will pull it off in the direction it is tipping 
in.  It will likely still rise, but horizontal motion is wasted energy.  
You will need to experiment to get the right balance, probably by adding 
weight to the light side.

	If you want to attempt to build a model with a tail rotor, what you 
probably should do is anchor the rubber band somewhere in the middle.  Then 
one end would be for the main rotor and the other for the tail rotor (the 
longer section should be for the main rotor).  How you attach the rubber 
band to get power to the shafts of the rotors is your big design decision! 
 There are a number of options.  Hopefully your teacher can help, or if you 
get really stuck, e-mail me and I'll give you some ideas.  Or you can use a 
big fin on the tail and use air resistance to limit spin.  You will lose 
some energy to spin, but you would be able to use the whole rubber band for 
the main rotor.  The last configuration, the double rotors, is the most 
complicated but I bet you would get huge design points.  You could use half 
the rubber band for the outer drive shaft and half for the inner shaft.   
The big trick there is how to support the shafts.  You would need a couple 
of rotating bearings, one of which would have to fit inside of the outer 
shaft to support the inner shaft!  Might be hard to find in such a small 
scale.  If you could figure it out, however, I bet it would be very cool!

	Anyway, my last bit of advice is to complete the building of it at 
least a week in advance so you can experiment and work out any bugs.  It is 
frequently not the best design that wins these competitions, but one that 
is simple and has had plenty of testing.  Good luck and if you need more 
advice or want some math equations to help describe stuff, e-mail me 
privately at brad@jymis.com and I will try to help.

BK