Missing Formula ?????

[Bill Gruby]

 

    I know this "Formula" exhists, I had it on file. For some reason I cannot find it again (CRS). It is a "Formula" for calculating the estimated speed in MPH of an engine running in the test stand. I remember that it uses the pitch of the prop and the RPM of the engine but that is all. I am starting a very large project and will need this "Formula" before I complete it. I would like to put this "Formula" back in my file. Can anyone out there help me out on this one?

   "Billy G" 

   Addition:  Is there anything you cannot find in cyberspace? In a search of Model Aircraft Static Engine Speed I found this link:      http://pages.sbcglobal.net/limeybob


          Find "Calculate"----Click on "Airspeed"----Fill in Engine RPM and prop pitch and click calculate. Viola Static Airspeed. At 30K an 11 pitch does 312.5 MPH Static---- Minus 30% for airframe drag thats 250 MPH in the air. WOW ! If someone has the formula I would still like to have it----Thank-you.

[Dick Fowler]

RPM X Prop Pitch X .000947

That's obviously the theoretical speed.... real world is usually less.

[Bill Gruby]

   Thank-you Dick, yes I realise this is theoretical, but it will meet my needs for now. I just checked to see if the link was close, it is right on the money.

   "Billy G"   

[Warren Leadbeatter]

Is there a prize for getting it right? 

How about this:

Airspeed Calculation:
This is an approximation based on the propeller pitch and engine rpm. It assumes that the rpm of the engine increases enough in flight to make up for the fact that thrust goes to zero at the calculated airspeed (based on static rpm measurement). It also assumes that you have done a reasonable job of matching your engine and propeller to the plane.

Velocity in miles per hour = 9.47E-4 x RPM x Pitch

Where:
RPM = propeller speed in revolutions per minute.

Pitch = propeller advance rate in inches/revolution.

[Bill Gruby]

     NOPE NO PRIZE   

    You got me, please explain 9.47E-4  ?

     "Billy G"     

[Warren Leadbeatter]

Hi Billy,

I tested it, it works. Seems pretty accurate too based on my flight data.

9.47E-4 is 9.47 x 10^-4  ( or 9.47 times 10 to the power of minus 4)  or 0.000947

I think the "E" means Exponential

I was pretty good at maths once. 

[Bill Gruby]

   Warren:

   Thank-you, Thats the same as the first one only harder.   

   "Billy G"   

[Warren Leadbeatter]

Sorry - I didnt notice that Dick had put his answer in the subject line until after I posted mine. 

[Bill Gruby]

   Warren;

  Nuttin to be sorry for---Yours sounds more mathematically(thats a 50 cent word) superior. 

    "Billy G"   

[Dick Fowler]

   Warren;

  Nuttin to be sorry for---Yours sounds more mathematically(thats a 50 cent word) superior. 

    "Billy G"   

Hey... I'm a simple man. What more can I say! 

[Bill Gruby]

   Hey Dick, Thats OK so am I besides anybody that paints -----Never mind, we won't start that one again, we almost got canned the last time.   

   "Billy G"   

[Paul Taylor]

G-Man,
By the subject I thought you were needing the formula for moon-shine.
 

[Bill Gruby]

   NOPE---Just need to do some calculations for the big guy. It's still an inside 'Brotherhood" joke so don't nobody ask. We ain't tellin yet. You will all find out soon enough.   

        "Billy G"   

[Paul Taylor]

I know.....

I still say you guys are over the top.

[Bill Gruby]

   



                                      ITS NOT NICE TO THROUGH STONES 


       "Billy G" and "Uncle Phil"   


Also, The US Government has proven without a doubt that I am 100% over the top, I have papers to prove it   

[minnesotamodeler]

Hey be careful who you're threatening to throw around.

--Ray Stone

[minnesotamodeler]

Don't think it works for extremely low-pitch props.  My .061 with a 6x2 hits somewhere around 50-55 mph on the stopwatch; reverse-formulaizing says that would be something like 30,000 rpm--don't think so.   Besides, where does diameter fit into this picture?  I can get the same rpm with a 5x3 as a 6x2, which the formula says would be 85 mph! Again, I don't think so...

So, what am I missing?

--Ray

[Bill Gruby]

   Ray;

    Prop Diameter only makes a difference in the RPM, bigger prop lower RPM. It is not needed in the equation. I needed this formula to get an idea how fast my Fox .78 would run on different props, sorta give me a place to start looking for the ultimate run, so to speak. My .78 will turn a 14/5 at 11,000 RPM. Using the equation:

                                          11,000 X 5 X .000947 = 52.085 MPH--- Theoretical

                                          11,000 X 5.5 X .000947 = 57.2853 MPH-- Theoretical

   Which prop would you rather start with ? Again this is only a "Guesstimation" but it is somewhere to start rather than "Blind".  But then again I could be talking total nonsense but it does kind of make sense.

   "Billy G"   

[Paul Taylor]

   



                                      ITS NOT NICE TO THROUGH STONES 


       "Billy G" and "Uncle Phil"   


Also, The US Government has proven without a doubt that I am 100% over the top, I have papers to prove it   

Over the top it not a bad thing - Like throwing stones. It is a good thing.

Like remember when "Your Bad!" was the same as "Your cool!"

Having young kids around the house they bring home all the new young hip sayings. I am not sure when the call me an "Old Fart" if that is a good thing or not. They bust out laughing as they leave the room.

[Dick Fowler]

Don't think it works for extremely low-pitch props.  My .061 with a 6x2 hits somewhere around 50-55 mph on the stopwatch; reverse-formulaizing says that would be something like 30,000 rpm--don't think so.   Besides, where does diameter fit into this picture?  I can get the same rpm with a 5x3 as a 6x2, which the formula says would be 85 mph! Again, I don't think so...

So, what am I missing?

--Ray

IMHO probably a thrust versus drag issue. The greater the drag the less the prop will "unload" so speed is lower than the theoretical speed. This would be even more true for small engine/prop combinations where the amount of thrust is somewhat limited. An additional consideration is that a lower pitch prop doesn't have a large delta AoA of the prop blade  as speed varies so thrust min to max is not very large.

[minnesotamodeler]

   Ray;

    Prop Diameter only makes a difference in the RPM, bigger prop lower RPM. It is not needed in the equation. I needed this formula to get an idea how fast my Fox .78 would run on different props, sorta give me a place to start looking for the ultimate run, so to speak. My .78 will turn a 14/5 at 11,000 RPM. Using the equation:

                                          11,000 X 5 X .000947 = 52.085 MPH--- Theoretical

                                          11,000 X 5.5 X .000947 = 57.2853 MPH-- Theoretical

   Which prop would you rather start with ? Again this is only a "Guesstimation" but it is somewhere to start rather than "Blind".  But then again I could be talking total nonsense but it does kind of make sense.

   "Billy G"   

I'm not disparaging the approach, just trying to make sense of it...an engine will turn a smaller dia., larger pitch prop at the same rpm as a given large dia., small pitch...my .061 turns a 6x2 and 5x3 at about the same rpm, and yes, it's faster with the 5x3, but not THAT much faster (55 mph with one; 85 with the other? uh-uh).  Seems to me the formula is most workable when comparing same diameter, different pitches (so, different rpm)--or maybe same pitch, different diameters (again, different rpm); dealing with only one propeller variable.  Maybe throwing two variables at it at once skews the result?  Someone help me out here...

--Ray

[minnesotamodeler]

IMHO probably a thrust versus drag issue. The greater the drag the less the prop will "unload" so speed is lower than the theoretical speed. This would be even more true for small engine/prop combinations where the amount of thrust is somewhat limited. An additional consideration is that a lower pitch prop doesn't have a large delta AoA of the prop blade  as speed varies so thrust min to max is not very large.

In other words, it doesn't work for extremely low-pitch props? Where did I hear that before...?

--Ray

[Bill Gruby]

  Now ya done it, I'm lost? I ran some numbers for a 2 and a 3 pitch prop. I used 20K RPM and 30K RPM.

                     1)   20000 X 2 X .000947 = 37.88 MPH             3)  30000 X 2 X .000947 = 56.82 MPH

                     2)    20000 X 3 X .000947 = 56.82 MPH           4)  30000 X 3 X .000947 = 85.23 MPH

  2 and 3 are the same, but the difference in the two RPM ranges is weird? Now it's going whacko to me and I started this thread.

      "Billy G" 

[minnesotamodeler]

Thank you for making my point.

[Dick Fowler]

  Now ya done it, I'm lost? I ran some numbers for a 2 and a 3 pitch prop. I used 20K RPM and 30K RPM.

                     1)   20000 X 2 X .000947 = 37.88 MPH             3)  30000 X 2 X .000947 = 56.82 MPH

                     2)    20000 X 3 X .000947 = 56.82 MPH           4)  30000 X 3 X .000947 = 85.23 MPH

  2 and 3 are the same, but the difference in the two RPM ranges is weird? Now it's going whacko to me and I started this thread.

      "Billy G" 

I guess I don't see the problem. Just a fine example of the communicative property of multiplication. (2 X 3 = 3 X 2). Don't take the numbers too seriously. The assumptions are that the pitch is accurate and the media (air) behaves as a solid for the purposes of this calculation... we know that both of these are not quite true.

[Bill Gruby]

   Dick;

  I don't have a problem with that part, That is self explanitory. The problem comes with what looks to me as the lower you go with the pitch the less efficient the prop becomes. What the heck did I do now answer my own question?


    "Billy Mudd G"   

[minnesotamodeler]

The problem is it is inaccurate nearly to the point of meaninglessness.  The plane/engine I am using as an example is clocked pretty consistently at around 55 mph with a 6x2 prop.  Formula requires it to be turning 30000 rpm (with 100% efficiency) for that to happen; but 20000 is more likely.  Then you go to a 5x3 prop, still in that 20000 rpm range, and formula says it hits--wonder of wonders!--that same 55 mph or so.  Compare the (2) and (3) above.  I can believe everything there except the 30000 rpm.  (2) is probably reasonably accurate; (3) is wildly off.

I repeat: It doesn't seem to work for extremely low-pitch props.

Of course, there is another possibility, maybe more likely: That my 6x2 APC is in actuality a higher pitch!  figure it as a 6x3 and it looks closer; of course then the rpm won't match that of the 5x3, so the problem is still there, just shifted down. 

Incidentally, I see less than 10 mph difference, more like 5, between the 6x2 and a 6x3.  Again the formula does not predict that; more like 30. 

I wish it worked; it would be a valuable tool.  Maybe for higher pitches it's OK.

--Ray

[Mike Spiess]

Ya know I hated math (and all the other subjects in highschool) You guys are scaring me

[Dick Fowler]

Judging from the comments on another thread, it seems that complicated answers to complicated questions are received with something less than enthusiasm.

Deleted in the interest of cerebral health... mine!


Wild Bill, I understand completely.

[minnesotamodeler]

Well...in the real world, guess I'll just keep on swappin' props at the field  'til I find one that works.  I like to work out a lot of things on paper but this apparently ain't one of them for me.   Dick, I appreciate your efforts at educating this pore ignorant misplaced Okie.  Fascinating stuff but apparently beyond my ability to wrap my head around it.

--Ray

[don Burke]

In the full scale world designs including propellors are calculated and wind tunneled to death before construction.  But the proof of the pudding is in the flight.  Thank goodness!  Real world experience proves or disproves theoretical ideas.   

   

[L0U CRANE]

Bill, Dick, Ray and Don,

A basic way to predict the airspeed from a given RPM and pitch is:

Pitch x RPM, corrected to whatever 'units' you are comfortable with. It's that simple.

Say 12,000 RPM and a 4" pitch...

Feet per second is a useful condition.

We start with how many revs per second: R(/sec) = RPM/60. For the example, that's 12,000/60 = 200

Then consider how many feet per revolution: that's 4/12 = 1/3

So, fps = 1/3 x 200 = 66.667 fps

Since 60 MPH is 88 fps, 1 MPH is 1.467 fps, and (dividing 66.667... by 1.467) that's 45.54 MPH

Now, pitch:

Dick F has provided excellent sketches of prop sections and pitches. However, there's another thing to consider:

Most of our props have either a flat or undercambered 'rear' face. That is, they have a flat -(or undercambered)- bottom airfoil.

BOTH cases provide lift when the airflow is parallel to the bottom line of the section! ALL airfoils have a "zero lift" Angle of Attack - or angle to the airflow passing over them. Symmetrical airfoils have this 'zero lift angle' parallel to the chord line (defined as the longest single straight line from leading ede to trailing edge). Other, cambered (defined as having a curved midline between top and bottom surfaces) airfoils provide lift when their bottom line is parallel to the air passing over them. They must be turned "down," relative to the airflow, before they produce no lift. The angle where they produce no lift is their zero lift angle.

Raul Hoffman's book (available from AMA and elsewhere) Model Aerodynamics Made Painless is badly titled. It is a horror to make sense out of, but there is a way shown to estimate the zero lift angle of an airfoil: bisect the angle between upper and  lower surfaces at the trailing edge!

A look at a symmetrical airfoil shows that the zero lift angle is on the chord line. For other airfoils, it isn't. Props, mostly flat bottom airfoils, have a few degrees of positive Angle of Attack when the airflow is parallel to the bottom surface.

This may be part of why stunter  props, at low loads, seem to fly faster than the V = n x P (velocity = nr of revs x distance per rev) that we started with.

Sure, props "slip" - i.e., don't move through the air the way a metal screw with the same angles would  through a metal nut - but the difference from trhe zero lift angle to the rear face (where we usually measure prop "pitch" ) might account for that.

For example, assuming a prop unloads the engine so we get a 10% RPM increase from stalled, zero-motion (launch) conditions to level cruise after a lap or so, it seems usual that the timed lap speed is up to 120% of "prop advance rate" (RPM X pitch, converted in units). Anyway, these are numbers I've come up with over many years, and they seem to be useful. Accurate? Maybe not. Useful? Yep.

(If an error is consistent, it is as good as precise accuracy, no?)

After all this, the original question was how does prop pitch affect performace? Try it this way: An engine designed for RC use at 15,000 RPM is at less than ideal conditons at 10,000 RPM. Finding a prop that allows, say, 12,500 RPM in flight should get us closer to the engine's best power zone. Lugging it down to 10,000 RPM might just put it below its best torque response range.

So, go flatter pitch to get he "happy RPM" fpr the engine, at reasonable laptimes for CLPA.

[minnesotamodeler]

Thanks, Lou.  One thing I get from this is that prop "pitch" is sort of a relative thing...depending on what part of the blade you're actually measuring: Flat back side (bottom surface of A/F)(typical I guess) or the zero lift AoA. So the acting pitch may well be (is) more than the measured pitch.   Huh. 

Interesting.  That makes me more confident in believing real-world performance over claimed pitch (i.e. a "6x2" prop that performs more like a 6x3 probably is). Then the pitch stamped on the blade is only meaningful within that particular brand, assuming they measure all their props at the same reference point. So it's still trial-and-error for me. You can never know 'til you try it!  Especially, I guess, when mixing brands/styles. 

That's one more constant out the window. More and more, Aerodynamics looks like "Art" rather than "Science". At least I can still rely on the diameter being exact.

--Ray

[Alan Hahn]

Just to add some more noise to this issue.
I've been playing around with my electric SuperClown and props--trying to find a combo that flies well and at the same time uses less battery power. I started off with the recommended 9-4 prop, turning 12k rpm on the ground, and 13500 in the air (I have an on-board Data Recorder from Eagle Tree).

Well great I thought, if a 9-4 prop does that, then I can scale the rpm by pitch to get the same airspeed (and lap time). First try failed miserably--I had predicted 9000 rpm to be the target pitch, but actually needed 10k to fly  .

Anyway to make this long story shorter  , I tried props ranging from 9x4.5 to 9x9 (all APC thin-electric series), and clearly this simple pitch scaling didn't work anywhere. I always had to use more rpm than the simple pitch scaling would indicate.

Then by chance I talked to a couple of people (Al Kelly and Kurt Krempetz) and they mentioned a few things that turned on a light in  my head  .

What is was was air volume. Using this pitch formula really would work only for a screw in a piece of wood. What you are doing is calculating the rpm which would produce the same angle of attack for the prop blade for a constant forward speed and a variable rpm. The problem is that a 9-4.5 prop turning 12k rpm will produce more air volume (or thrust as we normally think about it) than a 9x6 prop at 9krpm, even though this is how pitch would scale to rpm. It would be equivalent to the lift of a wing at different airspeeds, but the same angle of attack. Obviously the higher airspeed would give more lift.

So as I pondered  , I realized that if I wanted to turn a prop at lower rpm (presumably more efficiently), I needed some way to compensate for the missing thrust. Well two things come to mind--increasing diameter and/or increasing the number of blades, or increasing blade width... What I had in hand was an APC 10x7 thin electric prop (2 blade). It is very similar in shape to the APC 9xX props, pehaps also a little wider.

Yesterday I flew the SuperClown with the 10-7 prop, at 8500 rpm (flying rpm) and it flew as well (airspeed and tension) as the 9x7.5 APC prop at 9200rpm (flying), but used less power in flight than the smaller prop.

So what really matters isn't solely pitch etc., but the thrust at approximately 50-60 mph airspeed. It would be nice to have some info about this. I remember an old post from someone who had access to a wind tunnel. This would be a nice thing to measure. You could set up an electric motor to power various props and record both rpm, power draw and thrust. How about it?

[Phil Bare]

Kind of interesting that  a 6" pitch prop turning at 10,000 RPM figures out to be 56.82 MPH with no slippage factor figured in..... Isn,t that close to the speed that we like for our stunt planes to operate at? Any way, an interesting question comes to mind......Will a 12"X6" turning 10,000 RPM  be slower, the same, or faster then lets say, a 10"X6"  turning the same 10,000 RPM.........??........Does tip speed play any part?? 

[Dick Fowler]

Kind of interesting that  a 6" pitch prop turning at 10,000 RPM figures out to be 56.82 MPH with no slippage factor figured in..... Isn,t that close to the speed that we like for our stunt planes to operate at? Any way, an interesting question comes to mind......Will a 12"X6" turning 10,000 RPM  be slower, the same, or faster then lets say, a 10"X6"  turning the same 10,000 RPM.........??........Does tip speed play any part?? 

It will be faster.

[Leo Mehl]

Seeing you are over the top when are you going to hit bottom. Cool Man.