max speed computation

[Gary Retterbush]

Knowning prop pitch and RPM it would seem one could easily compute max speed (disregarding all the fine print). Why doesn't it work? Is this another bumble bee mystery?

In fact, max speed was much higher than it should have been.

Okay, RPM goes up a little in flight but no where near enough to give a 50kmh difference.

[steve lewin]

I imagine if you know the inflight rpm, the actual effective pitch as opposed to the almost random number written on the prop and then you remember to factor in the wind speed at the correct altitude, assuming you're measuring ground speed not air speed, you could get quite close. Of course that computation would tend to indicate that gliders always have a top speed of zero ;).

Unfortunately I've never been able to persuade the universe to disregard the fine print ;).

Steve

[Ollie]

Just to elaborate a bit on Steve's comments. Every prop pitch measuring device I have seen measures the pitch of a line tangent to the bottom of the prop's airfoil. The true geometric pitch should be based on a line through the leading edge of the airfoil. The difference is about two to four degrees, depending on the airfoil. In addition to that, the cambered airfoil of the prop has a zero lift angle of attack which is negartive a few degrees. In other words, the prop can produce thrust at a much higher pitch advance than it is rated for.

Gary,
Without knowing how you measured the airspeed, what the measured airspeed was, how you calculated the top speed based on prop pitch and RPM, how you estimated the RPM in the air, etc. it is very hard to judge your conclusion that 50 KPH is too big a difference..

[Gary Retterbush]

Okay, I know all about printed prop pitch not being the most accurate in the world but still it should get one in the ball park.

The calulation I did was to take the prop pitch times 2.54 (convert to metric), times RPM, times 60, divided by 100000 and that gives kilometers per hour.

To measure the actual ground speed on a nearly windless evening at 20C at 300meter MSL we used a surveyers tape to measure the field which was 171 meters long. Two stop watches were then started by one person at the same time. One watch was then positioned at one end of the field and the other watch at the other end of the field (2 people). The plane flew at full power at approximately 10 meters altitude across the course. As it crossed the start end one watch was stopped and as the plane flew past the other end the second watch was stopped. The difference between the two watches is the elapsed time to a pretty fine measurement. This was repeated in both directions and numerous times. The field length of 171 meters was then divided by the time and this gives meters per second. Mulitply this by 3.6 and we have kilometers per hour.

So, Ollie that is what I did. Now I have played with the figures and it is darn difficult to get the actual difference of about 50 kmh.

EDITED:
I forgot to mention that if I assume some prop "slippage" the difference is of course bigger.

[Ollie]

Gary,

No measurement or assumption is complete without some probable error associated with it. Each of the individual measurements and assumptions should have a probable error assigned. Then add up the effects of all the probable errors to see what is the maximim accumulation of probable errors that is possible. Knowing the specified pitch of the prop would help assess how many RPM the motor unloads in the air. Motors with high pitch props unload more than motors with low pitch props for example.

You still haven't told us what your measured air speeds were. Fifty KPH is a lot bigger percentage of 60 KPH air speed than it is of 120 KPH air speed.

It would not be unusual for the reaction time of one stopwatch operator being 0.2 seconds longer or shorter than the other stopwatch operator. The assessment of operator reaction time error depends on the flight time over the course which in turn depends on the airspeed being measured.

Until you have done such a detailed analysis of all such probable errors and assumptions, it is premature to draw any conclusions.

Another benefit of a detailed error analysis is that it tells you where your experiment needs to be improved and how much the improvement will be.

[rorywquin]

Originally posted by Ollie

SNIP
It would not be unusual for the reaction time of one stopwatch operator being 0.2 seconds longer or shorter than the other stopwatch operator. .

My dad once won a court case on this basis. He was caught in a speed trap (bad in the days when they used stop watches) and his speed was calculated to be exactly 38.675 mph (or something) .

His arguement was, that it was impossible for two people using stopwatches to be accurate to within a 1000th of a mph! The magistrate agreed and let him off.


Sorry to get off topic !

[Gary Retterbush]

Ollie,
I know you are trying to be helpful but it is not nearly as complicated as you would make it. I am not sending my friend Buzz back to the moon, just trying to calculate the speed for a model. ;)

The measured speed was 165 kmh and the estimated speed was about 110. The prop pitch was 12 inches. BTW, the engine was a 3W140. EDITED: 3W160

I am well aware of reaction time error in using a stop watch but the method I used is very accurate; try it some time and see for yourself. Besides, a couple of tenths over 170 meters does not make a big difference.

The engine used normally gains around 200-250 rpm in flight.

[Ollie]

From what little I know of the experiment, I estimate a probable error of 10% for using the prop pitch specification, an 8% timing error, 5% for using static RPM and I haven't included sighting error, course measurement error, etc. Even with this cursory analysis, I can account for 23% of the difference between your calculation and your data, whose difference is 50%, Gary. That only leaves 27% unaccounted for. What if my error estimates are too conservative? Some of these error estimates may or may not cancel each other but, in the worst and, somewhat improbable case, the errors may all be additive.

[Gary Retterbush]

Ollie,
The prop is going to be measured for pitch. A professional who knows his business. BTW, measuring pitch correctly is rather complicated as it depends on diameter. I won't go into that as that is not my field.

As for timing error, it is less than 2% maximum. Course length was measured with a surveyers tape which should put that error to less .003 %.

RPM (static and flying) is pretty well known with the 3W engines but I'll accept your 5% for that one.

If you could see the sighting set up you would agree that it is less than 1%.

All in all, no where near the 23% you came up with.

My conclusion at this point is the effective pitch has to be a lot more than the stated pitch.

BTW, you are assuming that all errors are in the same direction which is unlikely.

Time will tell.......

[vintage1]

Er...what? everybody has missed the most fundamental point.

The airframe drag. You still need to be bgeneratuiing thrust at max airspeed to overcome the drag. That means you may never get anywhere *near* the pitch speed.

What you attemp to do is to pick a prop that is generating the most thrust at the anticipated top speed.

Otheriwise its like saying 'my car engine will do 7000RPM, so if I fit an overdrive 5th gear it will do 200mph' Trouble is WILL you engine do 7000RPM pushing that car along at that speed.

No.

If you fire up Motocalc, and enter realistic figures for the airframe, you can plot drag and thrust versus speed for the model, and that is a far better way to get to a first guess at how fast it will go, and what prop will make it go the best speed. My models are usually estimated to be topping out at 80-90% of the STATIC pitch speed, and only about 75-80% of teh actual pitch speed once the motor has revved up and the prop unloads.

Example, little warbird that is in there at teh moment.

7x5E prop revving at 10,800 rpm static giving a pitch speed of 51mph.

According to Motocalc, this combo will max out at 49mph at which point the RPM has risen to 11,900 rpm., and the prop is now delivering just 4oz of thrust, which is the calculated drag of the airframe at that speed.

If I put that combo in a WWI bipe tho, I doubt it would get to 30mph :) Too much drag.

[Gary Retterbush]

vintage1,

The error is in the other direction so drag is not in play. The plane is actually faster than the calculated pitch speed by a large amount.

If you would like the data for Motorcalc I can see about giving you the info for a 3W160 4 cylinder turning a 30 inch X 12 prop at around 6000 RPM in an Extra which weighs right at 20 kilos fully tanked.

[vintage1]

Which doesn't answer the original question of how come it went faster.

Lots of explanains all to do with prop pitch (as stamped) not being pitch (as measured by various fudge factors)...but heres another thought.

How did ou enter the timing run?

The BEST way toi ge super fast speeds on a level course is to haul the model up inti a wingover, come down in a steep dive, and level off....and then pull up at the other end, trading speed for height, and do the same back again.

Heck, an unpowered glider can do over 150mph like that allegedly :)

If there is any wind shear or thermals aboit, that can do good things as well, if the model is in lift, you need to effectively dive it to mainrtain level flight.. :)

[Gary Retterbush]

There was no attempt to go fast. There was no diving or other funny business, just a nice straight flight thru the trap. If you note earlier posts you will see than it was of an evening with almost windstill and a rather normal temp and pressure altitude for here. Again, this is an attempt to see why the actual speed is so darn much higher than it should be.

[Dick Huang]

Gary,
[QUOTE]Originally posted by Gary Retterbush
[B]vintage1,

The error is in the other direction so drag is not in play. The plane is actually faster than the calculated pitch speed by a large amount.

vintage1 is correct unless your airplane has a drag of zero.
I would run M-cal or E-cal with various drags until you get 165 KPH and 110KPH V max with plots of thrust & drag vs. speed. What is the zero thrust air speed? Is it less than 110 or 165 KPH? IMO prop pitch speed may or may not have something to do with V max.
Dick Huang:)
P.S. Also Ollie's error analysis should be used to help explane the difference.
P.S.2 the performance in M-cal or E-cal should be corrected to the same AGL and ambient temperature for comparsion purposes.
:D

[Gary Retterbush]

Dick,

Drag would only be a factor IF the actual speed was less than calcuated pitch speed. That is not the case. Prop slippage is also a factor but again only in the other direction.

Certainly drag and prop slippage and a lot of other things are in play but NOT the cause of why the plane is faster than it should be. EDITED: I repeat; the plane is faster than calculated! END OF EDIT Normally we have the reverse and then the drag factor and slippage etc etc can help explain it.

I have considered Ollie well thought out error analysis but as I noted most are well below what he figured.

BTW, the zero thrust airspeed is zero!

[jrb]

Many folks often miss this; but propellers add velocity to the approaching air, as shown in the AE notes below.

So it is possible for a plane to fly faster than the prop's pitch speed.

Most, if not all, propeller aircarft that hold speed records did and prove this to be the case.

[Gary Retterbush]

Dick,

It finally dawned on me what you meant when you asked about the zero thrust airspeed. If my math has not totally failed me it is 238kmh. Sorry for being so dense!

That is based on the aircraft speed of 165kmh and a 30 inch (.762m) prop turning 6000 rpm.

[Dick Huang]

Gary,
1) I'm talking about a thrust available vs. thrust required analysis as a function of velocity; the velocity at which they meet is the maximum velocity of that airplane. Look in any text on airplane performance analysis.
2) Do a propeller thrust analysis as a function of velocity;at 0 velocity (static) the thrust is the largest and continues to decrease till it reaches 0 at some value of velocity. The velocity where thrust required and thrust available are equal is the Vmax velocity and nether is zero!
Dick Huang

[Gary Retterbush]

Dick,

I did the prop thrust analysis and that gave me 238kmh as I stated in my previous post.

However, I think we are getting afield from my basic question of how the plane can be about 50% faster than the pitch speed.

[vintage1]

Wel, assumng no other errors, the plane was producing thrust way above the (geometric) pitch speed....how did you measure the in-air RPM anyway?

[Gary Retterbush]

I did not measure it in flight. As I said previously, it is rather well accepted that a 3W160 gains about 200-300 rpm in flight. To get up to the speed that was actually measured the rpm would almost have to increase by about 50% over the static which is impossible. Those 4 cylinders will not hack 9000RPM!

[vintage1]

So what prop was on it, and what RPM was it doing?

Might as well check the data and calculations...

[Gary Retterbush]

Same as I told you before: 30 inch X 12 inch turning 6000 RPM static and assumed 6200-6300 in flight.

[vintage1]

well, either the prop has better than 16" effective pitch, or the RPM was up around 9000, or a little of both, or you have a patentable invention I'd say :)

[Gary Retterbush]

Exactly my point! I know the engine can not turn more then 6400 absolute max but it is hard to believe the effective pitch is around 18. 18 is about what would be required and then the prop slippage and drag would have to be very low.

This entire subject came about because one of the guys in my club used a radar gun to check speed and got almost 180 kmh. I did not believe that and started my measurement procedure and came up with 165 kmh. I had also calculated roughly what the pitch speed should be and was very surprised to find it was way off.

[Dick Huang]

Gary,
Not trying to beat it to death but from what you have provided if we can make the following table:
Velocity(KPH) Thrust(lbs or N)
238 0
165 ?
110 ?
0 ?
and If we assume thrust and total drag are equal at max vel of 110 and 165 KPH, what is the difference in thrust and therefore drag (thrust required) at 165 KPH and 110 KPH? The difference in drag will give you an idea of how good your drag estimate was. This analysis may help you explane the difference in max vel.
Dick Huang:cool:

[Gary Retterbush]

Dick,

All you say is true and valid. However, it still does not get to the crux of my basic question which is: how can actual top speed be so much more than pitch speed.

We can do the math you suggest and validate that there is enough thrust to overcome drag up to a point. It is obvious that we have enough thrust to get to 165 kmh. As I have been brain washed by the "pitch speed group" that is what determines VMax assuming drag, prop slippage etc will decrease that somewhat. As a result I am wondering where the "bad apple" is?? :)

[Ollie]

It might be as simple as the factory or some subsequent practical joker just stamping the wrong pitch number on the prop. Until you measure the pitch you can't be sure.

What about possible aeroelasticity of the prop? Is it possible that the prop is twisting to a higher pitch under load? If the center of twisting rotation is far enough behind the aerodynamic center of the prop airfoil then the leading edge upward torque could overcome the nose down pitching moment of the prop's airfoil.

You don't explain what physically limits the RPM to 6,400.

I prescribe a very healthy dose of scepticism for ALL measurements and assumptions, especially the ones you are most certtain of.

[Gary Retterbush]

Ollie,

The prop is a Menz and is pretty darn stiff. That is not to say it is not twisting in flight but one never knows.

The engine is just not physically capable of turning much higher without coming unglued! This is not a Ferrari that can turn 18000 and live to tell about it! ;)

You wrote: I prescribe a very healthy dose of scepticism for ALL measurements and assumptions, especially the ones you are most certtain of.

Hmmm, I am pretty certain you know what you are talking about. Should I rethink that, too. :rolleyes: Just pulling your chain. :D

[markdrela]

Originally posted by Gary Retterbush
how can actual top speed be so much more than pitch speed.


If the prop has thick cambered blade airfoils, their zero-lift angle offsets add to the net effective pitch angles. So the aerodynamic pitch, which is defined from the zero-lift lines and thus defines the actual pitch speed, can be considerably larger than the geometric pitch.

For example, the common Graupner 6x3 folding prop actually has an aerodynamic pitch of about 4". So the pitch speed which is (correctly) determined using the aerodynamic pitch is a whopping 33% larger than the bogus pitch speed determined using the 3" geometric pitch.

[Gary Retterbush]

Mark,

The blade is not highly cambered. To get a pitch speed that is about right the prop would have to be around 18 minimum. Since it is suppose to be a 12 that is a pretty fair discrepency. However, I am more and more of the opinion that the effective is a lot higher than I first thought or even suspected.

My prop expert is away for a few days to a big scale event but I should have his opinion of the pitch next week. In the meantime I'm going to try to get my new Zero into the air.

[markdrela]

Originally posted by Gary Retterbush

The blade is not highly cambered. To get a pitch speed that is about right the prop would have to be around 18 minimum. Since it is suppose to be a 12 that is a pretty fair discrepency. However, I am more and more of the opinion that the effective is a lot higher than I first thought or even suspected.


It doesn't have to be "highly cambered" to have a big effect. A typical prop blade airfoil might be nearly flat-bottomed and 10% thick. For such an airfoil the zero-lift line will be about 4 degrees above the bottom surface from which pitch is typically measured. Knowing this zero-lift angle "a_ZL" one can then reliably estimate the effective pitch with the following formula:

P_eff = tan{ artcan[ (P/D)/2.5 ] + a_ZL} 2.5 D

An example: Let's say you have a 20x12 prop,
and assume a_ZL=4 deg. Therefore...

P = 12"
D = 20"
P/D = 0.60
P_eff = 15.76"

That's a 31% increase from P to P_eff.

[vintage1]

So, we get 31%? over the 110km/h - that takes us up to 144 km/h, and we only need to unload to 6800 RPM to get the last 14% discrepancy.

I'd say that somewhere in there is the answer. the zero thrust pitch speed is maybe 40% higher than the geometrical pitch.

That ties in with a few other things I have been puzzled by - people reporting flying at pitch speeds that Motocalc says are so near stall speed that it couldn't possibly work...

[Gary Retterbush]

For what started as a friendly but heated discussion in my club about the speed of a given model has turned into an informative theme, at least for me.

I just had a very pleasant chat with the maker of the 3W engines and have learned that he normally figures about an 8% RPM increase in the air versus the static measurement. This is somewhat more than I had previously been told and thus gives about 6500 RPM for the case in question. (Ollie, you're right again!)

The actual prop in question will get a good look/see next week when my “expert” returns. However, I do know that the it is not unheard of for the props of a given diameter and pitch from the maker in question to give a 400 RPM static difference due to slight pitch variances.

Mark,
Just eyeballing a prop about like the one used, I would guess (repeat: guess) there is in fact about 3 degrees. This afternoon I am going to cut the prop at the 70% length and then I can get a better look at the section. I must be even more crazy than my wife always says when I go cutting up a brand new prop!

Slowly I’m closing in on the theoretical pitch speed that would be required but then comes the drag and prop slippage etc which drop the speed again. Dick, I may have to do your calculations after all. :)

[Dick Huang]

Gary,
Using Dr. Mark Drela's formula for effective aerodynamic pitch, Peff and inputing D=30 in, P =12 in and RPM=6400. I get Peff=17.44 in. which translate into a pitch speed of 170.1 KPH (105.7 MPH).
Are you glad you started this thread!
Dick Huang
:D

[Gary Retterbush]

YES!!!:D :D

If nothing else, I learned a couple of things (a lot more than I figured on when I started).

I thank all who participated!

Gary

[Sparky Paul]

I'd like to see the prop cross-section after the cut...
I have a moderately damaged 18x8 I could do that to.

[Gary Retterbush]

Sparky,

For you I will even send you the prop if you want it and that's no joke.

Give me an address and it will be on the way. Direct mail: gary.retterbush@t-online.de

I was wondering where you were hidding during the past few days. ;)

Gary

[Gary Retterbush]

Just in case anyone else wants to see the section of the prop here it is: (this is NOT the actual prop in question but very much the same)

[Ollie]

Gary,

I downloaded the image of your last post, printed it out and did some measurements on that prop's airfoil.

Assuming the manufacturer measured the prop pitch by the usual method of using a tangent to the bottom of the airfoil as a reference, the difference between such a reference line and the geometric chord line of the prop's airfoil is about 3.5 degree plus or minus about 0.25 degrees. The mean camber of the airfoil is about 2.6% plus or minus about 0.1%. This camber should result in a a zero lift angle of attack of about minus 2.1 degrees plus or minus about 0.2 degrees.

Therefore, the angular difference between the reference line the manufacturer probably used to measure the pitch and the zero lift pitch of the prop is probably about 5.6 degrees plus or minus about 0.45 degrees at the diameter that the prop was cut.

The pitch angle at the cut is 15 degrees or so to the prop disk. The zero lift pitch angle is 20.6 degrees or so.

The pitch advance is proportional to the sine of the pitch angle. The sine of 15 degrees is 0.259. The sine of 20.6 degrees is 0.352. Therefore, the error due to the difference in pitch advance is about 36% for this case. For lower pitch angles near the tip of the prop, where most of the thrust is produced, the percent difference in pitch advance will be much greater, asuming that the airfoil is similar near the tip. It is not safe to assume that the prop was designed to have a constant, zero-lift pitch over its diameter.

My general conclusion is that the manufacturer's pitch rating for a prop should not be used in pitch advance calculations without further measurements and evaluation at a number of stations along the diameter of the prop.

[Gary Retterbush]

Ollie,

Thanks for doing the math for me!

I always knew that printed pitch was a joke but I am a little surprised to find out how big of a joke!

At any rate, I think the original question I had has been pretty well answered.

[Sparky Paul]

I sawed off a Zinger 18x8 last night at 4 stations.. here's
one.
The pitch is reasonably 8 inches at each station...
4,5,6,7 inches from the hub.

[Sparky Paul]

And at 7 inches...
The Zinger is almost a flat-bottom, so the effective pitch will be close to the stated value, but less that the true pitch at the zero-lift line.

[Gary Retterbush]

Sparky,

That is interesting. I have not used a Zinger for a long time and had forgotten how they are cut. The prop I chopped up is cut such that the pitch is constantly changing as one goes out the blade (it is getting less).

[Sparky Paul]

Gary, I get this from your prop... measure where it's cut and fird the circumference, and then the geometric pitch using the tangent.

[Gary Retterbush]

Here are two more cuts:

First one at the 50% point and the second at the end.

[Gary Retterbush]

The end. Note how the pitch (EDITED: should read angle) has decreased.

[Sparky Paul]

The change in pitch on the prop is normal... as the diameter increases, the distance per revolution increases, so the angle of advance decreases...
On the Zinger I cut last night, at 4", the angle is 19 degrees, the pitch works out to 8.6"
At 5", the angle is 15 degrees, pitch 8.4"
At 6", the angle is 12 degrees, pitch 8.0"
At 7", the angle is 10 degrees, pitch is 7.75"
Measure your prop and determine the radius where it's cut to find the pitch equivalent to the angle.
For this type of photo, it's best to fix the camera/object distance, so nothing changes in the view. Moving the camera around alters the perspective and the angles of the blade..
A scale in the picture helps also..

[Gary Retterbush]

Sparky,

Yes, I know that the apparent pitch should change. In the first picture you posted of the Zinger it looked like it was not doing so. The later pictures showed that was not the case.

The last 2 pictures I posted were taken without much effort late last night. I usually set up the tripod for this type of picture plus a light or two. I did try to get the shot pretty square on to the cut and the hub.

[steve lewin]

I'm sure you guys know what you're talking about but the use of pitch and angle as if they mean the same thing is confusing me. Just to clear it up this less educated person (it's been fascinating following this thread and I've learned lots) :

We're talking about the *angle* of the blade reducing as you get further out along the prop in order that the *pitch* remains constant. This is because the *pitch* is related to the *angle* and *diameter* at the specific point on the blade.

Is that right or am I still confused ?

Steve

[Gary Retterbush]

Sounds good to me, Steve.

I edited one post to reflex angle versus pitch. You are very correct that I was using the two as if they were one and they are not. Thanks for pointing that out.

[vintage1]

Yup Steve. The blade section goes round 2 x pi x R every revolution.

If the pitch P is a constant, the angle is arctan P/(2 x pi x R) for any given radius section.

An easy way to visualise it is to think of a stack of square section lengtht of wood twsited sligthly....at the root the pitch angle is steep, at the tips, less so.

In fact, that is one of the better ways to make a wooden prop, starting from that,

[Gary Retterbush]

This is the way I used to make the props for my Sopwith:

[Sparky Paul]

50 years ago... about the same age as that photo.. :) (back when 25 cents was 25 cents)
I carved a couple of props from pine sticks. And discovered there's a reason for the shape. A constant width/constant angle prop doesn't work... especially on an .049.

[Gary Retterbush]

Sparky,

Be careful! You are dating both of us! :rolleyes:

[Sparky Paul]

As if anyone else would! :)