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Sep 26, 2009, 11:02 AM
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Quote:
Originally Posted by Ken Myers
Drive Calculator uses the same type of prop constants as the Emeter.

You can download it here
http://www.drivecalc.de

and get the constants
Hi Ken,

I downloaded Drive Calc, and I can't seem to find where the prop constants are listed. How do I get them to show?

Chuck
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Sep 26, 2009, 12:35 PM
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Ken Myers's Avatar
Click on Edit in the main menu, select propeller. There will be a drop down menu with all the props in it. It shows both the constants for thrust and absorbed power,
Sep 26, 2009, 12:39 PM
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Quote:
Originally Posted by Ken Myers
Click on Edit in the main menu, select propeller. There will be a drop down menu with all the props in it. It shows both the constants for thrust and absorbed power,
Aha!!!!!!!!!!

Here's a screen shot of a GWS 7x3.5 prop.

Which of the constants would be the ones I'm interested in; that would be what the 'prop constants' are?

Thanks for the help with this!

Chuck
Sep 26, 2009, 02:23 PM
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Dr Kiwi's Avatar
While we are on the subject... like Chuck I'm wondering exactly which numbers of those displayed here to use... how do these Drive Calc constants match up with the numbers Motocalc uses... it uses "P constant" (ranging from something just over 1, to as high as about 1.8) and "T constant" (typically close to 1, sometimes slightly >1, other times slightly <1).

Bruce Abbott has listed a lot of Prop Constants in the Motocalc format: http://homepages.paradise.net.nz/bhabbott/props.html
Last edited by Dr Kiwi; Sep 26, 2009 at 02:28 PM.
Sep 26, 2009, 04:33 PM
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flieslikeabeagle's Avatar
The "classic" way of doing this is to use the Abbott equations. These basically assume each little segment of the prop blade makes lift (thrust) and drag in the usual way, like any aerofoil (lift = 1/2 rho CL V^2 S, drag = 1/2 rho Cd V^2 S). Integrating the lift over the entire length of the rotating prop blade gives you the prop thrust, and integrating the drag along the blade length gives you the torque needed to turn it, from which you get the power needed to turn it.

If D is the prop diameter, P its pitch, and N its rpm, you end up with something like this:
Power = K1 x P x D^4 x N^3
Thrust = K2 x P x D^3 x N^2

In those two equations, K1 is the power constant, and K2 the thrust constant. Simple enough, if we just pick a system of units (preferably SI units) and leave the equations alone. Unfortunately, RC hobbyists don't like leaving things alone, and US hobbyists prefer the nightmarish Imperial units, so K1 and K2 ended up being broken into two parts; one part has a value close to unity (like those Motocalc P and T constants), while the other part absorbs the rest of K1. In other words, we replace K1 with something like K1 = C1 x E1, where C1 is close to 1.0, and E1 is whatever number is necessary to make C1 close to 1.0.

There is one more complication; if the prop blades are heavily twisted, some parts of the blade (near the root) make very little thrust when the prop is static (not flying through the air at speed). To account for this, you first calculate the props pitch/diameter ratio P/D. If this number is less than 0.6, do nothing; if the number is greater than 0.6, replace P with an effective pitch, Peff, given by Peff = 0.6 x D, and put this effective pitch Peff into the thrust equation (but not the power equation).

Martyn Mckinney has previously posted the exact equations he uses in his spreadsheet prop calculator to RCG:
Quote:
Originally Posted by Martyn Mckinney
STATIC POWER = K X P X D^4 X RPM^3 X 5.33*10^-15 WATTS

STATIC THRUST = K X P X D^3 X RPM^2 X 1.1*10^-10 Oz.
In the power equation you can see that Martyn has broken what I called K1 into two parts, his constant "K" and the fixed number 5.33*10^-15. This is done so K has values between about 0.5 and 1.6 for most typical 2-bladed props.

Similarly, Martyn's second equation breaks what I called K2 into two terms. the constant "K" and the number 1.1*10^-10.

Here are links to two of Martyn's posts on the subject:
https://www.rcgroups.com/forums/show...60&postcount=9
https://www.rcgroups.com/forums/show...5&postcount=11

Strictly speaking, the Abbott equations apply only to props with absolutely rigid (no flexing) blades of infinite length. This is because the lift and drag equations we started with apply to rigid, infinitely long wings - they do not include the effects of tip vortices, which always appear when you have a finite length wing or prop blade.

One of many nice things about these Abbott equations is that they let you make educated guesses at unknown props, because the equations scale with diameter and pitch and rpm in a predictable way. If, for instance, you know the value of K for an APC 13x6.5 E prop, you can make a good guess as to the performance changes that will result from using an APC 13x8 E prop in its place - just replace P = 6.5 with P = 8 in the equations, assume K hasn't changed, and Bob's your uncle.

This sort of guess will not always give you an exact answer (K does vary a bit from prop to prop, even within the same prop family), but it may well be close enough for practical purposes. And if it isn't, you make a few measurements, calculate K for the new prop, and you're up and away.

-Flieslikeabeagle

Edit: As far as I can see, Martyn is using the same constant K to predict both thrust and absorbed power, rather than using separate constants for thrust and power. I think this works exactly only if we assume the lift/drag ratio for every propeller is the same. However it is probably "close enough" most of the time. (Martyn, if you read this, would you chime in, please?)
Last edited by flieslikeabeagle; Sep 26, 2009 at 04:45 PM.
Sep 26, 2009, 04:51 PM
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Drivecalc's constants are independent of prop diameter and pitch, whereas Motocalc includes the prop dimensions. The advantage of including dimensions is that the constants can then be normalized around 1.0, rather than varying greatly depending on the prop size. A rough power constant conversion can be done with the following formula:-

Motocalc P.Const = Drivecalc Power Factor / ((Diameter/12)^4*(Pitch/12)*0.9)

Unfortunately Drivecalc also has a variable Power Exponent, whereas Motocalc uses a fixed exponent of 3.0. If the Drivecalc exponent for a particular prop is not 3.0 then the formula should also include rpm (I have not yet worked out how to do this). Even then, if Motocalc predicts an rpm significantly different from what was used in the conversion, its calculations will be off.

Thrust Constant conversion is harder because Motocalc uses a non-linear formula to derive it. Also, once again Motocalc uses a fixed exponent of 2.0 to predict thrust, whereas Drivecalc has an extra variable. It might be easier to simply manually adjust Motocalc's thrust constant until it predicts the same thrust as Drivecalc does at the same rpm.
Sep 26, 2009, 05:07 PM
Registered User
Quote:
Originally Posted by NoFlyZone
Aha!!!!!!!!!!

Here's a screen shot of a GWS 7x3.5 prop.

Which of the constants would be the ones I'm interested in; that would be what the 'prop constants' are?

Thanks for the help with this!

Chuck
For thrust, it's

A * ((RPM/1000)^B)

So, for 5000 RPM, you'd have

1.542 * ((RPM/1000)^2.188) = 52 grams of thrust.

For power INTO prop, you'd have

0.021 * (RPM/1000)^3.055 = 2.8W

Using the same technique, peakeff gives 52.3g and 2.59W

http://www.peakeff.com/beta/Calculators.aspx

This method is EXACT. It's a curve fit of measured data. It captures the prop flexing at different RPMs. If you take 4 or 5 points and curve fit it, there's no need to measure thrust anymore. If you know the RPM, you know the thrust. And if you know the RPM, you know the torque, just as if you were measuring the prop on a torque balance. Assuming you trust the source of the numbers of course. But Kiwi's numbers form the basis for most thrust measurements. And the torque figures came from a calibrated DC generator. For all all intents and purposes, this stuff is pretty darn good.

What Motocalc does is totally different. Motocalc approximates an entire series of props with a few numbers. Unfortunately, it's very hit an miss. It cannot even begin to capture the difference between props in the same family.

http://www.peakeff.com/beta/Calculators.aspx
Sep 26, 2009, 05:26 PM
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flieslikeabeagle's Avatar
Edit: Bruce Abbott and Matttay both posted while I was composing the following post. Therefore there is some overlap in the material.

As we saw above, the Abbot equations start with theoretical knowledge of airfoils, use some math to turn that to theoretical predictions for propellers, and finally condense it all down to prop pitch, diameter, rpm, and a couple of numerical constants.

That approach has some great advantages, including the ability to extrapolate from data we have already measured to predict performance data we don't yet have. I gave a simple example of a prop size change above. However, more complex extrapolations also become possible; for instance, the Abbot equations allowed me to mathematically derive the result that you can make more thrust at the same pitch speed using the same input power if you are willing to gear down and use a bigger prop. This is one of the key realizations that drives my motor calculator software, WebOCalc.

Phil Maur, who measured props for Hyperion/Aircraft World, took another approach entirely. Consider a propeller as a black box, something we know nothing about - no aerodynamics, no physics, none of that. All we know is that it takes power to turn, it takes more power to turn it faster, it makes thrust if we turn it, and it makes more thrust if we turn it faster.

Taking this black-box approach, Phil measured the rpm, thrust, and power required to turn the prop; he did this for various props at various rpms, and ended up with a huge mass of measured data. Note that he didn't just measure thrust and rpm - he also measured the power needed to turn the prop at each rpm, by measuring the back-torque on the motor housing while it was spinning the propeller. It's an approach used in all engine and motor dyno's, but very few hobbyist propeller measurements include this additional measurement.

Now, with the measured data in hand, turn back to that first idea that it takes power to turn the prop, and more power to turn it faster. Knowing this, we can write a very general mathematical equation that connects the two things we know: the power put into the prop, and the rpm at which it turns:
Power = Const1 x rpm^const2

Notice that we assume NOTHING; we don't assume how the power varies with rpm, or prop pitch, or prop diameter, or prop rpm; we don't assume the blades are rigid, or they make lift proportional to the square of their velocity. Instead, we just plug in the most general mathematical equation we can, and then numerically fit the measured data to the equation to come up with the actual value of the two constants.

Phil measured the rpm in 1000's (to make the numbers more convenient), and with that small change you end up with the following equation for power:

Power(watts) = Cp*(rpm/1000)^Pf.

Cp is the "Power coefficient" and Pf the "power factor". If you compare this equation with the Abbott equation for power, the Abbott Equation uses "3" where Phil's equation uses "Pf". That numerical "3" is based on the assumption of rigid, endlessly long prop blades, as we saw earlier - by replacing it with "Pf", a number that is nearly, but not always exactly 3.0, Phil came up with an equation that allows for flexing prop blades, finite blade lengths, and other real-world prop size and rpm dependent variations. If we have good measured data for a prop, Phil's equation can fit more exactly to the subtleties of that data than the old Abbott equation can.

In exactly the same way, we can create a general thrust equation:

Thrust (grams) = Ct*(rpm/1000)^Tf.

Where Ct is the thrust coefficent for the propeller, and Tf the "thrust factor". Compare with the Abbott equation for thrust, and you'll see that Tf is exactly 2 in the Abbott equation; in Phil's equation, Tf is nearly (but not always exactly) 2.0.

As far as I know, these two equations are what are used in the Hyperion E-meter, in Rod Badcock's "Thrust XL" calc program, in Drive Calc, and probably in some other motor/prop software as well.

As we've seen, Phil's equations let you do a very good job of mathematically representing the measured performance of a specific propeller. Unfortunately, that ability to accurately represent one specific set of measured data comes at a price: because we made no initial theoretical assumptions about propellers, we are also unable to extrapolate to any other propeller using Phil's equations.

In other words, if we know Cp, Ct, Pf, and Tf for an APC 13x6.5 E prop, it tells us absolutely NOTHING about an APC 13x8 E prop. It tells us absolutely NOTHING about how an APC 14x7 prop might behave. It tells us NOTHING about the efficiency of bigger props vs smaller props. All it tells us is what an APC 13x6.5 E prop does...nothing more.

So: the good thing about Phil's approach is that it is a very good way to mathematically represent a specific propeller that has been comprehensively and accurately measured. And the bad thing about it is that it is utterly useless to represent a propeller that has not yet been measured - you can't really extract any sort of extrapolation from it.

A third bad thing about Phil's method is that not many people have the equipment to make that all-important motor torque measurement along with thrust and rpm; as a result, you'll not find too many 3rd party prop measurements out there - most if not all of the data contained in the E-meter seems to have come from Phil's own measurements, despite the several years that have elapsed since they were taken. And while Phil measured a great variety of props, there are an even bigger number of props out there that he did not measure, including many popular APC and GWS sizes, as well as newer prop lines that have appeared on the market since Phil did the original measurements.

I'm not sure if any of the Drive Calc developers have made more recent prop measurements along the lines of Phil Maur's measurements. I hope they have, otherwise this clever and useful approach to the mathematical representation of propeller performance will continue to get gradually more out of date as time goes by and more props appear on the market with no corresponding Cp,Ct, Pf, and Pt coefficients available for them.

-Flieslikeabeagle
Sep 26, 2009, 05:38 PM
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Geeeeze,

What a fascinating journey into the world of props!

I'm going to print this out and study it until it clicks. I'm sure to have a few questions along the way, but this should give me a great overview of what's going on behind the scenes.

Thanks Beagle !!!!!!

Chuck
Sep 26, 2009, 05:50 PM
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flieslikeabeagle's Avatar
Quote:
Originally Posted by matttay
This method is EXACT. It's a curve fit of measured data.
It most certainly is not exact! It may be more exact than the Abbott equations, sure. It may even be as exact as we need for practical purposes, given inevitable manufacturing variations in props.

But it cannot be mathematically exact. There is no guarantee that the prop performance can be represented by a single exponential equation, no matter what the value of the exponent is. You can only represent it exactly using a power series with an infinite number of terms.

There is a mathematical theorem that says you can fit any data set with N measured points using a polynomial of order N-1. Therefore, if you make, say, 4 measurements on a prop at 4 different rpms, you can exactly represent those four measured data points using an equation of the form:

power = Cp0 + Cp1 * rpm^Pf1 + Cp2 * rpm^Pf2 + Cp3 * rpm^Pf3

Assuming zero thrust at zero rpm (a safe assumption) lets you get rid of Cp0, but you still need the other three terms to be exact. And even then, there is no guarantee that the equation will represent the propeller in between the measured data points, much less allow you to extrapolate beyond them. It is possible, for instance, to make a numerical fit that is exact at every measured data point, but which oscillates wildly above and below the data in between those measured points!
Quote:
Originally Posted by matttay
And the torque figures came from a calibrated DC generator.
Can you tell us more about this? The photos I saw of Phil Maur's original setup showed a digital scale set up to measure back-torque of the motor spinning the propeller - no separate DC generator in sight. Are you referring to (newer) measurements you or someone else made?
Quote:
Originally Posted by matttay
What Motocalc does is totally different. Motocalc approximates an entire series of props with a few numbers.
Yeah, Motocalc appears to use the Abbott equations, but also assumes that K is the same for one entire family of props, i.e., that all APC Thin Electric props have the same value of K, for instance. That turns out to be quite far from the truth.

As Martyn Mckinney and Louis Fourdan have shown with their prop and motor calc software, if you use a specific thrust and power constant for each individual propeller size (and not an entire prop family), the old Abbott equations are still quite usefully accurate.

-Flieslikeabeagle
Sep 26, 2009, 07:02 PM
Registered User
[Rats, somehow I edited this message instead of posting a new one. Beagle, hopefully you saw it before I messed it up. The short summary was:

1) I didn't claim it was mathematically exact. Like most formulas in physics and engineering, they get you really, really close by simplifying complexities such as friction.

2) The DC generator I've always assumed was just a golden motor with a known torque constant (which is related to the KV). Once you know the torque constant, you know the torque required to spin a prop at 5 amps, for example, and IF the motor current is much greater than Io, even better.

3) I argued the per-family prop constants are very poor compared to per-prop method. ]
Last edited by matttay; Sep 27, 2009 at 02:22 AM.
Sep 26, 2009, 07:55 PM
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Dr Kiwi's Avatar
Like Chuck... my poor brain is spinning.....I need a series of rainy days to digest all this information... however I do, dimly, see where we are going! I've been fudging Motocalc constants for years in an effort to improve their fit to my measured data!
Sep 26, 2009, 11:02 PM
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Bruce Abbott's Avatar
Quote:
Originally Posted by flieslikeabeagle
Motocalc appears to use the Abbott equations, but also assumes that K is the same for one entire family of props, i.e., that all APC Thin Electric props have the same value of K, for instance. That turns out to be quite far from the truth.
Motocalc actually has 8 different 'generic' settings for APC props, so it's not that bad. Of course generic settings are not as good as individual constants for each prop, but Motocalc does allow you to enter these into its database (it just doesn't come with them pre-loaded).
Quote:
Pf [is] the "power factor" ... the Abbott Equation uses "3" ... Tf the "thrust factor" ... is exactly 2 in the Abbott equation
Motocalc usues the same simplification, and this is where it may depart from reality enough to require 'fudging'. I have dyno tested a few props and I found that using exponents of exactly 3 (for power absorbed) and 2 (for thrust produced) gave very accurate predictions. However I only tested my props at low power levels. At higher power levels the prop blades may bend forward and/or twist, changing the effective pitch. Making the exponents variable gives a closer fit over a wide range of power levels.

However, having these extra variables does not guarantee better results unless you have accurate torque and thrust measurements. Although you can derive the power constant by calculating the motor's output power, this adds another potential error source. Most of my constants have been derived using Motocalc. Of course we all know that Motocalc is not always very good at this. Drivecalc should be better because it accounts for non-linear motor and prop response, but it also fails sometimes. In practice therefore, significant inaccuracy is likely.

But the question is:- just how accurate do you really need to be? Most testing is done with hobby grade instruments that have low absolute accuracy, and secondary factors are often not taken in account (eg. air pressure and temperature, thrust stand design, manufacturing tolerances). Reproducibility may be quite poor. Calc programs also have limited accuracy, even when provided with very accurate 'constants'. Then you put the power system in a model and it all goes out the window!
Sep 26, 2009, 11:26 PM
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Quote:
Originally Posted by flieslikeabeagle
As far as I know, these two equations are what are used in the Hyperion E-meter, in Rod Badcock's "Thrust XL" calc program, in Drive Calc, and probably in some other motor/prop software as well.
Note that this does not apply to Motocalc's thrust calculations. It calculates thrust directly from power, not from rpm (if you change the power constant, thrust will change even when rpm is held constant). This point may seem moot because theoretically the results should be the same, no matter how it got there. However in practice Motocalc often under-estimates rpm but still manages to get the thrust right.
Sep 27, 2009, 02:23 AM
Registered User
Here's a comparison of measured data, predicted data, and Motocalc data.

For motocalc, I used

P Const = GWS HD = 1.07
T Const = Generic = 0.95

The measured data came from Dr. Kiwi xls he shared with me. You can see the bumps in the blue markers. My guess is that the blue dots aren't smooth due to measurement anomolies, not because the prop is doing something weird at slightly different RPM.

But, take a look at the predicted thrust in red. You'll see just about everywhere it agrees with measured data within 1%.

Motocalc is the other trace. It's not even close.

Where Motocalc predicts 7000 RPM gives ~330 g (which requires 25.6W into the prop), the measured data says to get 500g it requires 45W.

This means there's a massive power error floating about in motocalc whenever the user picks GWS HD props of about 15/45 = 30%.

I think we can all live with errors around 5-10%. But 30% is getting really unusable, especially if you don't know where the error is falling (left or right of curve). It's a 60% window...

And the comical part of it all is that Motocalc allows to select from HUNDREDS of airfoils. It allows you to select a finish of film or dope. I can only imagine the poor user that sits around carefully tracing his wing profile, and holding it up to those in books and webpages, trying to guess his airfoil correctly to ensure his answer in Motocalc will be "right". And then when Motocalc gives him a crappy answer, the user figures "Man, I must have picked my airfoil incorrectly"

It conveys such a sense of tedium to the user, and then it goes and massively blows it by "guessing" at the one area that matters just about more than anything else.

It's a joke. The Motocalc people ought to sell a dart and a poster with their offering...it'd probably let you get closer


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