A quick and fun prop math riddle

BigBadLou

BigBadLou

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Lou
If you feel like it, here is an interesting and fun math riddle about a propeller on a GA aircraft.
(if you don't like math, propellers, airplanes or have a negative attitude, feel free to vent your thoughts elsewhere, thanks)

Let's say:
- a bird happens to be in the path of an engine - and let's say the plane is a twin (so that there is more room around the engine and the bird has a better chance of escaping)
- the bird's altitude is above the engine cowling

Do you have a mental picture of the bird trying to fly right over the engine cowling but through the propeller circle?

Some numbers:
- the 2-blade propeller spins at 2400 RPM and the aircraft travels at 156 knots GS
- the bird is 1 ft big (for simplification) - such as 1ft wingspan and 1ft length

Now the interesting question is: into how many chunks would the propeller cut the bird up should they airplane continue on its path?

This question came to me one day while I was watching a video of a bird strike on a Baron. I came to thinking: if it had been a single, would a prop on the nose have helped "chunk up" the poor fella so that it would pose less risk of breaking the windshield and incapacitating the pilot or passengers?

I am posting this riddle knowingly in the Pilot Training section because
a) I didn't find a better section for aviation math
b) I think every pilot, including students, should know what path the propeller takes through the air

Disclaimer: no animals were hurt during me thinking of this riddle. :)
 
My calculations reveal a buzzard could get through without being chopped up.
 
Flying toward you increases his chance of passing through unharmed. Flying the same direction as you, his chances (of surviving) go down as his airspeed approaches the speed of the plane. This is only true if you catch him first.
 
Last edited:
BigBadLou said:
If you feel like it, here is an interesting and fun math riddle about a propeller on a GA aircraft.
(if you don't like math, propellers, airplanes or have a negative attitude, feel free to vent your thoughts elsewhere, thanks)

Let's say:
- a bird happens to be in the path of an engine - and let's say the plane is a twin (so that there is more room around the engine and the bird has a better chance of escaping)
- the bird's altitude is above the engine cowling

Do you have a mental picture of the bird trying to fly right over the engine cowling but through the propeller circle?

Some numbers:
- the 2-blade propeller spins at 2400 RPM and the aircraft travels at 156 knots GS
- the bird is 1 ft big (for simplification) - such as 1ft wingspan and 1ft length

Now the interesting question is: into how many chunks would the propeller cut the bird up should they airplane continue on its path?

This question came to me one day while I was watching a video of a bird strike on a Baron. I came to thinking: if it had been a single, would a prop on the nose have helped "chunk up" the poor fella so that it would pose less risk of breaking the windshield and incapacitating the pilot or passengers?

I am posting this riddle knowingly in the Pilot Training section because
a) I didn't find a better section for aviation math
b) I think every pilot, including students, should know what path the propeller takes through the air

Disclaimer: no animals were hurt during me thinking of this riddle. :)
Click to expand...

The bird may not get sliced up at all because there is more to this than just a rotating set of edges. The prop is creating air movement, LOTS of it. The bird may well simply jet stream thru the prop unharmed, or scathed a tad. The airflow, and air density will affect the outcome as much as anything, and the velocity of you toward the bird, and the bird toward you.
 
Would also need to know how fast the bird is traveling to get a closure rate. Also would be different if he entered the prop are right behind a rotating blade or right in front of a rotating blade.
 
The prop would only cut the bird in two if it managed to cut it in half at all.
 
tlglenn said:
Is the bird an unladen swallow?
Click to expand...

Sorry, you need to clarify.

unladenswallow.style.jpg
 
During the time the aircraft travels forward one foot, the length of the bird, the two blades combined will sweep through an arc of about 110 degrees. So the bird has about a 70% chance of making it through untouched. Or so it seems :wink2:
 
All great answers, I love 'em. :)
And I believe it was the African swallow. What is your favorite color? Blue. No, black. Wait, blue. :D

For this calculation, I considered the speed of the bird to be negligible (a pigeon, for example won't be flying 50 knots :) ).
 
Dihedral said:
During the time the aircraft travels forward one foot, the length of the bird, the two blades combined will sweep through an arc of about 110 degrees. So the bird has about a 70% chance of making it through untouched. Or so it seems :wink2:
Click to expand...

That is about what I came up with. Essentially the propeller is making about 1 revolution for every 6.4 feet of forward movement, or 1 blade every 3.2 feet.

Brian
 
Is the plane on a treadmill?
 
brcase said:
That is about what I came up with. Essentially the propeller is making about 1 revolution for every 6.4 feet of forward movement, or 1 blade every 3.2 feet.

Brian
Click to expand...

Well, neither of you guys have addressed the speed the bird is flying nor direction to calculate speed of relative motion.:nono::rofl:
 
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