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This may be a stupid question

  1. Oct 6, 2009 #1
    Hi, I have a question that has stumped me for a while, well its been a while since I have done any academic work and its annoying me that I just can't work it out.

    Here it is:-

    You have 3 propellers, we shall call them A, B and C

    Propeller A is a small propeller
    Propeller B is a medium sized propeller
    Propeller C is a large propeller

    the common fact is they all rotate at the same speed

    The quetion asked is:- If the shafts of these propellers are all rotating at the same number of RPM's, which propeller tip is travelling at the fastest speed.

    Now the answer is C, but why?

    Can anyone tell a stupid 40 year old why this is so, is there an equation that shows me this to be true.

    if it makes it easier for someone to explain lets say there was some measurements on the diagram.

    lets say the RPM's were 15
    lets also say that prop A, from centre of shaft to tip of blade is 0.5m
    lets also say that prop B, from centre of shaft to tip of blade is 1.0m
    and finally, prop C, from centre of shaft to tip of blade is 1.5m

    any help would be appreciated
     
  2. jcsd
  3. Oct 6, 2009 #2

    DaveC426913

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    The tips travel one revolution in 4 seconds.
    The distance they travel is the circumference, 2*pi*r.

    prop C's tip must travel farther around in the same length of time. To do so, it must move faster.

    So:
    prop A's speed is 2*pi*(.5) / 4 = ? m/s.
    prop C's speed is 2*pi*(1.5) / 4 = ? m/s.
     
  4. Oct 6, 2009 #3

    mgb_phys

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    Just think of drawing a circle on paper with a compass.
    Suppose you take 10 sec to draw the circle
    If you have a small radius (distance from the centre) then the pencil is moving very slowly over the paper.
    If the compass are opened full then to get round the larger circumference in 10secs the pencil will have to move more quickly.
     
  5. Oct 6, 2009 #4
    Okay guys thanks for that, I understand the compass, that I can relate to.

    I had a quick go using this:-

    RPM= 25 so 1xrev = 2.4 secs

    Prop A Radius: 0.5
    Prop B Radius: 1.0
    Prop C Radius: 1.5

    So in my understanding 2 x pi ( 3.14......) x 0.5 = 3.14 / Rev ( 2.4 secs ) = 1.30m/s
    2 x pi x 1.0 = 6.28 / 2.4 = 2.61m/s
    2 x pi x 1.5 = 9.42 / 2.4 = 3.92m/s

    So if above by my pathetic brain is correct then prop c does indeed have to revolve quicker to still rotate in 2.4 secs........but how?, how do you rotate a propeller tip quicker to maintain the tip speed in 2.4 secs without increasing the RPM, if the propeller is fixed to the shaft and all the shafts rotate at 25rpm's then just as a first quick thought if someone asked you this would be that prop A ( 0.5 ) would be rotating the quickest. I am really thick. I just can't grab the concept if the shaft rotational speed is a constant and unable to be changed surely prop A will reach say top dead centre again quicker than prop C which has further to revolve round to get back to TDC.

    Why do I feel so thick, someone slap it around my face until I get it..lol, no wonder at school 20 yrs ago, the teacher used to rap me over the head with knuckles until I either lied I got it because my skull was caving in or I did actually grasp the point.

    sorry to keep going on about this, you see when I think about the compass thing, yes to move the compass round a small circle in 10 secs it would be moving slowly, but to move it around a full larger revolution in 10secs yes it does have to go quicker but if the centre speed is constant how do I get it to go quicker??

    Sorry, I am really thick, anybody do home tutoring?? lol
    more to the point anyone still got the will to live or do you feel like giving me the knuckle thing again...lol

    cheers
     
  6. Oct 6, 2009 #5

    mgb_phys

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    They will all reach top dead centre after the same time - the angular rate (degrees/second) is the same.
    But if you were running along the ground pushing the outside of the prop you would have to go faster (in metres/second)

    Think of a clock.
    On your watch it takes 1 hour for the minute hand to go round 360deg. If the hand is only a 1/4 inch long then the speed of the tip is very slow and you can't see it move.
    Now imagine a huge clock on a building like Big Ben the hand is 20ft long and goes around in the same time but the tip of it is moving 20'*12" / 0.25" = 960 times faster.
    Now imagine a huge clock with hands a mile long - the tips of them would have to be moving at 6mph to get round in 1 hour - you would have to jog to keep up!

    You can see this with a sundial. a small garden sundial you can't see the shadow move. But if you have a very long shadow from say a skyscraper at sunset it can be moving fast enough to see it move over the ground.
     
  7. Oct 6, 2009 #6

    DaveC426913

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    If you lengthen the prop blades, say, from .5m to 1.5m and keep the RPM the same, then the tip of the blades will move faster. (It will take more torque to do so, you might need a more pweorful motor.)

    Think of it another way, you could have all three props affixed to the same shaft a thte same time. They'd all rotate at the same speed. But the tip of the largest prop will traverse a larger distance than the others.

    Why would you want it to go quicker?

    You've moved form a 'what would happen' to a 'how do I get this to happen' scenario.



    P.S. Please stop beating yourself up. You came here because you are looking for answers. That's what we do.
     
  8. Oct 6, 2009 #7
    Do you know, I have gone away from the problem and had my tea, and you know what.....I really am thick...that I do know for sure.

    I have managed to grasp it now, when i think of the clocks I can see it, and I was thinking that prop A was the fastest because it was the smallest, but in the equation evidence proving that prop C is travelling at a higher m/s it proves that the tip of C is actually going quicker than A.

    I appreciate all your help on this.

    Just one more quick question, if you only had 3 months to get a GCSE in Physics and now you can understand what my brain works like, what book would you recommend to me to try and get my GCSE, I need to get GCSE in Maths too, so I need something that goes straight to the basics and works from there. I am looking for a job and they say that the requirements are GCSE's in Maths and Physics etc, I just want to be prepared enough so that if I am accepted then the training/college work won't frighten me...talk about needing a more powerful motor...lol, if my brain was compared to a current day PC I am still in the ZX81 box thinking in black and white.

    I really do appreciate all your help on here and the fact even though I am somewhat disappointed that nobody has shouted at me for being thick.....lol....I know you are all probably sitting there thinking it, feel free to shout at me and call me names...lol

    thanks very much
     
  9. Oct 6, 2009 #8
    The image that popped in my head to describe this intuitively is a merry-go-round.

    Imagine a very large see-through merry-go-round. You are standing 1 foot from the center. You look down at the ground and note how quickly you seem to be moving around relative to the ground.

    Then you carefully walk all the way to the edge of this large merry go round and look down at the ground. You should notice how much faster you are moving relative to the ground.

    The merry-go-round is rotating at the same rate in both cases (spins per second), but the speed (meters per second) is greater when you consider a point further from the center.
     
    Last edited: Oct 6, 2009
  10. Oct 6, 2009 #9

    DaveC426913

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    I think you will not make a success of yourself as long as you are wasting all your energy on self-deprecation.

    Enough already.
     
  11. Oct 6, 2009 #10
    I think you have trouble differentiating speeds in terms of rpm and m/s. Just think about these two terms and clarify yourselves. Then come back to this question. When you have trouble understanding something, it shows that you haven't understood clearly, something "more basic".
    Let the shafts be initially at rest. If they are so accelerated such that they cover equal angles in equal intervals of time, then shaft with the larger propeller would have consumed more energy when it had reached the TDC compared to the other two. Reason is a higher moment of inertia.
     
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