REFLECTOR: Prop

Sat Dec 16 17:18:03 CST 2006

Kurt,

Your calculations work with the brakes locked.  See the below to calculate 
tip speed in motion.  Also note that you should never exceed .85 mach 
because the airflow over the air foil of the prop will put you over mach 
1.0.

Larry Coen

N136LC

TIP SPEED

Anytime the aircraft is in motion (and the propeller is turning, of course) 
the path of the tip of a prop blade through the air is a helix, and 
therefore, it's velocity (the "tip speed") is the vector sum of the 
rotational velocity plus the translational velocity, or the helical tip 
velocity (explained in detail below).

Maximum helical tip velocity is an important parameter for propeller 
selection. In the absence of specific data from the prop manufacturer, it is 
safe to assume that (a) the maximum prop efficiency will be about 87% (for 
any metal prop a non-governmental agency can afford), and (b) that the prop 
efficiency begins to decrease dramatically when the prop is operated at a 
helical tip velocity in excess of 0.85 Mach. That occurs because the local 
air velocity over the surface of the prop (near the point of maximum airfoil 
thickness) will reach Mach 1, and create a shock wave, separating the flow 
and dissipating prop energy.

That phenomenon is very easy to spot in a high speed aircraft which has the 
capacity to run the prop too fast. Here is an example. A few years ago, I 
was flying a Glasair-3 to an airshow. I was cruising at 13,000 feet, 2400 
RPM, wide open throttle. I was running a bit behind schedule, so in pursuit 
of a few more knots, I decided to operate at max power (2700 RPM, WOT). It 
was something of a surprise when I lost about 15 knots of airspeed. I set 
the RPM back to 2400, and regained the lost 15 knots. Later I did the 
calculations to verify that the loss was due to the sudden loss of 
efficiency. It was.

It is actually quite simple to do the arithmetic necessary to determine the 
tip Mach of a prop at a given RPM and true airspeed. First, calculate the 
helical tip velocity components.

The rotational velocity is the diameter of the prop times the RPM times a 
conversion factor. Again using KTAS as the unit of speed, the rotational 
velocity in feet per second is:

           Vr (ft / sec) 60),    or

           Vr (ft / sec) 
The translational velocity is simply the aircraft TAS expressed in feet per 
second, or:

           Vt (ft / sec) 
With the rotational and translational speed (in the same units, of course) 
you can easily calculate the helical tip speed:

           Vht 
Next, calculate the speed of sound (Mach 1.0). The speed of sound in air 
varies with the square root of absolute temperature ONLY, as defined by the 
following equation:

           Vs 
where k, g and R are constants (1.4, 32.17 and 53.34 for air) and T is the 
absolute temperature (°F + 460) of the surrounding air.

So, if you are at 13,000 feet on a standard day, the air temperature is 
12.71 °F and the speed of sound (in feet per second) is:

           Vs1            Vs1 
The Mach number of a given speed is simply:

           M 
Putting it all together in a specific example, suppose you are flying at 
13,000 feet on a standard day at a true airspeed of 240 knots and an 84-inch 
prop turning at 2700 RPM. Here is how to calculate your prop-tip Mach (using 
the simple equations above):

           Vr            Vt            Vht            Tip Mach 

  ----- Original Message ----- 
  From: NMFlyer1 at aol.com
  To: reflector at tvbf.org
  Sent: Saturday, December 16, 2006 2:04 PM
  Subject: Re: REFLECTOR: Prop

  Since I have a unique setup, I needed to adress the prop-tip speed as 
well. My high HP engine, lots of torque and the redrive complicated things.

  Since I had it.. I thought I would pass along the quick and easy formula 
to find tip speed for those that need it:

  Dia. of prop (in feet) x 3.14 x RPM of the prop. Divide that total by 88 tip speed.

  For reference, speed of sound at sea level is 761 MPH.

  In my case, a max takeoff engine RPM would be 5000, which gives me 2940 
Prop RPM.

  my 76" prop 

  To find the max RPM you can turn a prop (withought breaking the speed of 
sound):

  66,984 Divided by (the distance,in feet, your prop travels in 1 RPM)

  Ex: 66,984 over 18.84' (72" prop) 
  My case would be: 66984 over 19.896 RPM).

  Hope it helps.

  Kurt

  In a message dated 12/16/2006 9:06:43 AM Mountain Standard Time, 
MMurp16900 at aol.com writes:
    Subject Prop R.P.M.
    The other consideration is prop diameter and tip speed.
    If the tips go supersonic the prop will not be as efficient.
    some racing planes have short diameter props for that reason.
    Some aircraft have geared engines and the engine runs at a higher rpm 
and produces more power and the prop turns at munch lower rpm and higher 
pitch
    Mack.

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