Ask A Scientist© Environmental Earth Science Archive

name         Cheryl
status       educator
grade        9-12
location     MD

Question -   My students are designing and building an airship to fly
as fast and straight as possible using a rubber band powered propeller
and helium gas for lift.  I do not have any information on propellers for
them; such as most effective size of blade for size of ship, data on
pitch of blade, width of blades, even number of blades, most effective
arrangement of propellers, etc.  I have searched the Internet for answers
but found no good sites.  Where can we get answers?
-----------------
http://www.woodenpropeller.com/Basic_Propeller_Design.html
Basic Propeller Design
Google is fantastic.  If you do not use it, go to google.com
and download their task bar.  Google takes up to 10 words
in a search, no need for the small ones, as "and", "the" etc.
No need for the www, unless you are looking for a specific site.
My search was "airplane propeller design", there were 127,000 replies,
I picked ( http://www.woodenpropeller.com/)  which lead to
the above design information.

There was another site selling a machine for $ 4,000+ dollars
to "make a propeller".  So, the "by hand" construction may put you
into the deli minas of the Wright brothers.   Fulfilling a dream
is not easy.

Perhaps if you size the propellers, you can buy them, as opposed to making
them.

The helium may pose other safety issues, a search for all information
on handling it would be a minimum.  Not knowing your situation,
I do not want to discourage the use, but I would stress concern.

James Przewoznik
=====================================================
You might try perusing gab on RC airplanes.   There are various sizes and 
densities of them.
Or visiting hobby stores to see RC light planes, blimps, and helicopters.

The variables are pitch, diameter, blade-width ("chord"), and blade 
curvature ("camber").

Blade thickness is not too important.   They are mostly all pretty "thin", 
in principle.
Using enough thickness to get the needed blade stiffness usually does not 
hurt.
it just makes the blade's cross-section fancier, because it must be 
streamlined better than a thin, cut-out and curved sheet.
Once you add the curvature, it is subtle indeed.  Maybe not what you want 
for a do-it-yourself experiment.

Your best blade might be somewhere between:
   the sleek straight blades of an aircraft propeller and
   the fat, scoop-curved blades of a room-fan.

Look at the blades of the ultralight circular RC helicopters now being made.
   ( get a "Hobby People" catalog or visit their web site)
   (These have 3 or 4 blades facing upwards, placed 
 side-by-side.   Attitude control is by varying power to each blade.)
   Maybe even use some of them.
   They are typically thin Polystyrene foam sheet, cut to a shape with protruding 
 trailing edge, then the trailing edges are bent downwards for curvature.
   This kind of thing might work well for your blimp.  It is light, you 
 can make it yourself; you can make many different shapes and sizes.
   The only difficulties are finding sheet of the right thickness and 
 stiffness for your size, and making it keep the curvature you give it.

Newer helicopter models may be getting away from thin sheet, because such 
crude props are a little inefficient.
   Maybe they have that 5:1 thrust-to-drag ratio I mention below.

I do no't think the optimum design zone will be very small.
All propellers are wings flying sideways, in circles.
Wings have a lift-to-drag ratio of roughly 10: (20 if outstanding, 5 if 
terrible).
That is, if their angle of attack into the airflow is in the correct 
range: less than stall angle, and more than zero.

The pitch of the prop-blade is its diagonal twist, the angle near the tips,
relative to the tangent-line of the circle the tips travel.
The pitch is chosen so that this "wing" has a positive angle of attack on 
the air it is slicing through,
even when the vehicle moves forwards through the air.
Having a selection of angles of attack is your most important variable.
If pitch is too small, the spinning prop could actually slow down a 
vehicle being pushed by something else.
Then it could have more drag than the rest of the airframe.
If too large, you will be splitting air into vortices fore and aft or each 
blade,
  rather than smoothly fan-pushing the air backwards.
You might be able to feel the distinction by putting your hands near the 
prop while holding the blimp still.

Notice this implies the best pitch-angle will be lower at slower speeds 
and higher at faster vehicle speeds.
If your blimp is in a race from a standing start,
you might wish it could have lower pitch at the start than later when 
cruising at full speed.

It would be a cool dream to have spring-variable prop pitch,
With it, you could set the blade to have a high pitch when springs were 
relaxed, for cruising.
Then when the blimp was standing still and each blade feels a high angle 
of attack on the air,
The air pushes harder on the trailing edges, the springs give way, and 
each blade pivots or flexes to a lower angle.
However, I am not sure how often this is done.
The spring and hinge fixture for each blade is a significant complication
on what otherwise would be a single piece of solid material.

The length of the blades ("prop diameter") is next.
It is changed so the available force and speed and wattage from the motor 
(your rubber band)
matches the load (whether blimp-mass acceleration requirement, or air drag 
at steady top speed.).
Too small, the prop spins fast, wastes energy furiously churning air and 
does less than its best.
Too large, the prop's air drag is so large the rubber-band cannot turn it 
very fast,
and you might not succeed in using up most of your allotted power,
which you would prefer to do, to go as fast as possible.

I think you can find some sites by RC-model-airplane enthusiasts, and/or 
some forum talk.
Perhaps there is a hobbyist's book that covers this subject.
You should keep looking, because I am only spitting out ideas,
and you need some more specific arithmetic.

You would be best served setting up a spreadsheet to roughly calculating 
things like

given:                     prop rotation rate, diameter, pitch, vehicle's 
air speed,
                                       and for the wing-like cross-section 
 of your blade: thickness, width, CD and stall angle

guesstimating-->  angle of attack, blade's average airspeed, thrust

I think this is doable with a one-page spreadsheet and no math beyond 
trig-functions and algebra,
and maybe a hand-guessed look-up table for CD-vs-angle of attack.

It is just a wing, an airfoil.  Have them research that...
http://www.allstar.fiu.edu/aero/lift_drag.htm
http://www.pilotsweb.com/principle/liftdrag.htm
  look about right to me.

Also, for me, Google[propeller pitch parameters] got some beginning leads.
http://jsbsim.sourceforge.net/JSBSim/index.html
http://jsbsim.sourceforge.net/JSBSim/classJSBSim_1_1FGPropeller.html
http://www.planeandpilotmag.com/content/2002/nov/propellerbasics.html
http://www.skytribe.co.za/Props/propexcerpt.htm
http://www.mindspring.com/~thayer5/ffpages/tips/propcarve.html  -  on 
carving balsa props

Jim Swenson
=====================================================
Most designs of model aircraft are based heavily on successive
approximations where the designer tries a variety of ideas relying mainly on
his experience and common sense.  However, it is possible to gain insight by
a few simple physics calculations which can be used to guide one's insight
as well as to learn some physics.

Consider a "12x8" propeller rotating once a second.  Once this calculation
is done, we will show how to modify it for other propellers and speeds
quickly and easily.  First: a "12x8" propeller is 12 inches in diameters and
has a pitch of 8 inches; an 8" pitch means that in one rotation it moves
through 8 inches of air (if there is no slippage).  Equivalently, if kept
from moving it moves the air 8 inches.

A cylinder of air 12" in diameter and 8" long has a volume of
905 in^3 = 0.015 m^3.
(PLEASE CHECK ALL NUMBERS!)
Since the density of air is 1.29 kg/m^3, the mass of air in this volume is 
0.019 kg.
Since the air was initially at rest, the propeller gives the air a momentum
p = mv = 0.019kg*0.20m/s = 0.0038 kg m/s (8" = 0.20m).
So the force exerted on the air by the propeller (or equivalently by 
Newton's second law--action and
reaction) the force exerted on the propeller by the air is
F = dp/dt = 0.0038 kg m/1 s = 0.0038 N*0.225 lb/N = 8.5E-4 lb*16oz/lb = 
0.014 oz.

Now, if the propeller turns faster, say two revolutions per second, it moves
twice as much air and at gives the air twice the speed, so the force goes
like f^2, where f is the frequency in rotations per second.  So if the
propeller rotates at 10 revolutions/s, the force is 1.4 oz (10^2 * 0.014
oz).  The force also increases with the square of the diameter of the
propeller (since the mass of air accelerated does), so a 15/8 propeller
rotating at the same speed produces (15/12)^2 the force of a 12x8 propeller.
Finally, increasing the pitch of the propeller increases both the mass of
air accelerated and the speed given to it, so the force increases like the
pitch squared.  So a 12x10 rotating at the same speed will produce a force
(10/8)^2 as large as a 12x8 propeller.

I would suggest you pull the airship with a sensitive spring scale at the
desired speed to determine the force you need.  If you do not have a spring
scale, a rubber band works well.  See how much it stretches when pulling the
airship at the desired speed and then find the weight (in ounces) needed to
stretch the rubber band the same amount.

Finally, the design of the engine.  I presume you will use rubber to power
your craft.  You can find the spring constant of the rubber by stretching it
with a weight and using F = kx, where F is the weight, x is the stretch, and
k is the spring constant of the rubber,  Then estimate the energy given to
the airship in a flight of reasonable length, using W = Fx where W done
(energy expended), F is the force exerted by the propeller (see above) and x
is the length of the flight (do be careful with units (W = joules, F =
newtons, and x = meters).  Finally, guess how much the rubber is stretched
when you wind it up; the energy stored in the rubber is W = (1/2)k x^2.

If you use any of this, I would be delighted to hear how it worked for you.

Best, Dick Plano
=====================================================