EagleOne

Here's a small (I'm not so sure) article I wrote explaining how to calculate a prop's static and dynamic thrust. Read it and tell me what you think. Error corrections are also welcome

As soon as I get the FTP problems I'm facing solved, I will upload it to my website and I will let you all know.


A simple method to determine a propeller's static and dynamic thrust

This is a simple method which I developed for calculating a prop's performance. This method is not perfectly accurate (due to the assumption of a single lift curve for all propellers), but gives a good approximation of the thrust value with around 5-10% of error margin. For accurately determining the static thrust the most recommended method is to actually measure it, same for the dynamic thrust, but it's not that easy to measure the later.

First, let's begin by explaining that a propeller's pitch is the theoretical amount of forward advance in one revolution, as if it was a nut in a screw, with that said we can call it the geometric pitch. The aerodynamic pitch is the angle of attack (AoA or alpha) of the blade with the air-stream coming into it. The common denomination of propellers (at least for model aircraft purposes) includes the geometric pitch in inches, and that's measured at 75% at the length of one of the blades (.75 radius). But this number isn't proportional only to the AoA (aerodynamic pitch) as many people think, due to the nature of the pitch definition, it's also linked with the propeller diameter (or radius). Since any prop has an airfoiled section, we can determine the thrust (and the torque needed to spin it by using the drag, but that's not covered in this article) by calculating the amount of lift it produces based on the prop's airfoil lift coefficient, but since every brand of prop has a different airfoil, and bladewise speaking the airfoil changes it's incidence a lot, to accurately calculate the thrust gets really complicated. But this problem can be solved by using a generic lift curve (modified to account the incidence changes), which greatly simplifies the process.

Now, let's get to the equations. For the equations to work out, the SI units have to be used, so first you have to convert the prop's dimensions from inches to meters by multiplying them by 0.0254, also the speeds will be in meters per second (miles per hour * .447) and the thrust in Newtons (Pounds / 0.221). Since we are using the data at the 75% radius station, let's calculate what the radius is at this position:

R = (Diameter / 2) * 0.75

Now, let's calculate the geometric pitch angle (the blade incidence from the horizontal plane):

GP = Atan(GeoPitchDistance / (6.2832 * R))

We need to know how many revolutions the prop makes in a second, so:

RPS = RPM / 60

Now, we can proceed to calculating the rotating speed at .75 radius:

RV = 6.2832 * RPS * R

And the aerodynamic pitch (AoA) with FV being the forward speed of the aircraft in meters per second (obviously for static thrust it is 0, but in this method using 0 will lead to an error, so the smallest recommended number for FV is 0.5):

AP = GP - Atan(FV / SV)

Calculate the accelerated stream velocity:

ASV = FV / Sin(Atan(FV / SV))

Here we will calculate the lift coefficient by using the generic lift curve. For AoA's smaller or equal to 20 degrees:

Cl = (-0.00868 * AP2) + (0.21131 * AP) - 0.15734

And for AoA's greater than 20 degrees:

Cl = (-0.0000767 * AP2) - (0.000565 * AP) + 0.71244

Calculate the drag coefficient:

Cd = (0.000142 * AP2) + (-0.00671 * AP) + 0.19767

Before we go the thrust equation, we have to calculate the blade chord (which can also be measured at it's widest point, but most propellers have a blade AR of 6, so it's only a matter of dividing the prop radius by 6) and the air density at the altitude (in meters) which the prop is operating:

rho = 1.223 * 0.9 ^ (Altitude / 1000)

Finally, here's the thrust equation:

T = (NumberOfBlades * BladeChord * R * 0.5 * rho * ASV2 * (Cl * Cos(Atan(FV / SV)) - Cd * Sin(Atan(FV / SV)))) * 0.47

In order to make the calculation easier, here's a summary of the data you need to have in hand before solving the equations:

- Prop diameter in meters

- Prop pitch in meters

- The RPM at which the prop is turning

- The prop's number of blades

- Prop forward speed (is also the aircraft's forward speed)

A simple derivation from the Geometric pitch equation

This simple variation allows us to calculate with reasonable accuracy at which speed the prop would stop producing thrust, that also can be called the prop's max speed for a given RPM.

PMS = GeoPitchDistance * (RPM / 60)

Further notes on propeller behavior

By solving the equations presented above, we can see the reason for some important propeller behaviors. For example, why high pitch props have lower static thrust values (thus poor take-off acceleration and 3D flying performance) than low pitched ones (which give higher takeoff acceleration and better 3D performance). Or, by using the derivation from the geometric pitch equation, why low pitch props give slower top-end speeds when compared to high pitched ones.

crownvic

is this fact or fiction?

DBCherry

My Feedback: (4)

I have a thrust calulator program I can e-mail to anyone who wants it. The total file is only about 450 KB.
You plug in prop diameter and pitch, and engine RPM.

Maybe you could just post it on your site?
Dennis-

EagleOne

OK, let me explain it further.

I know there prorams that will calculate this, I even wrote one myself (I will soon be posting it), but I wrote this in order to explain how it works. For me it's not enough to see something working and say yeah, that's OK. I like to know how that thing works, and so I looked in various aerodynamimcs books and adapated some of the methods described there to simplify the process. As I said in the article also shows clearly the reason for many particular prop behaviors, which I find highly interesting. Then I thought it would be interesting to other people too. So I posted it here.
About the accuracy of the method, as I also said in the article, due to this being a simplyfied method you can't expect high accuracies from it, but it's an excelent starting point.

DBCherry,
You can e-mail me the program and I will put it on my site.
The e-mail is:
[email protected]

3DFanatic

My Feedback: (5)

ack, too much work. Just tie your plane to a fish scale for static thrust!

Tired Old Man

My Feedback: (1)

I'm with 3D Fanatic. Everything is getting way to complicated anymore. I firmly believe in the K.I.S.S methods.

Peter Khor

My Feedback: (4)

EagleOne, many thanks for taking the time to break down the explanation/math into manageble chunks. Please let us know when you've gotten a small program ready for ftp ... in the meantime, plugging the equation and numbers into Excel ...

In the meantime, there's another thrust program here:

http://www.bmaps.net/software/goodies.html

EagleOne

Today I received some very bad news regarding the FTP.

My computer's HD crashed a few weeks ago and I lost everything I had in it (except for what I had in CD backups), my whole website included (what I had in backup was a very small portion). So I couldn't connect to the FTP and I sent the admins an e-mila asking why...Well, they had a little problem and my account got deleted, and so my whole website.....[][] It's a free service (very good one BTW, without any ads and 50MB of space) so I can't complain about nothing, and I didn't lose money in the process just the time I invested to write it....So now I have do it all over again....

But anyway, we have to go over the problems we face and keep moving forward, so while I don't get the new website running, I will make a simple page with some downloads and a link to the article above. Maybe by tonight I will have it ready, I will let you know...

EagleOne

OK, I put a temporary front page up, so you can access the article and the program I wrote (I included with it the source code in C++, it's a very simple program indeed).

The article:

http://www.downwash.pop.com.br/propt.htm

The program (30Kb zip)

http://www.downwash.pop.com.br/propthr.zip

The site:

http://www.donwnwash.pop.com.br/

DBCherry, I will soon be posting the ThrustHP there.

Astro Fright

Nice work. I've been trying to figure out how to calculate thrust and torque for a prop without using empirical formulas. It seems the trick I was missing was the generic lift curve you came up with. How did you derive this curve? Are there any texts you have referred to that I may be interested in? I'm developing an optimization program for an electric airplane and I think this would greatly improve the accuracy.

EagleOne

The generic lift curve was generated by a rather empirical method. Looking at an airfoil's lift curve, the shape that closely resembles then is a parabola, and a parabola is the graph of a quadratic equation. So it was just a matter of putting the lift curve of a Clark-Y airfoil, which resembles most prop's airfoil sections and then the calculator gave me the equations to create the parabolas that most closely match the airfoil's lift curve. Then it was just a matter of adpating them to get thrust results close to the mesured ones on one of my planes (Enya SS 40 BB, 12300 RPM, MA 10x6 prop). From there I made an assumption that this would be close (note that I said close, so it's not exactly) to the real thrust for all props at all conditions. The lift curve is split in two parts because of their characteristic shape. Up to 20 degrees is one kind of parabola, after that is another, thus the 2 different equations.

p-51man

WELL, I have a slight problem that I hope you guys can help me with, i might have been procrastinating too long, but you may possibly be able to help me if anyone checks this post again. So the situation is that i have a science fair project due the 6th, and i dont know what units I should put the thrust in to. I pulled the plane with a fishing scale on the back, and I need to know what units of measure to put it in to, the scale was in pounds. Should i put the readings in to lb/ft sq.? or just simply pounds, i dont know how to do pounds per foot squared if that is in fact what i have to do , but if you can, please respond to this as soon as possible. thank you.

DBCherry

My Feedback: (4)

Your results should be in pounds (of thrust). Using per square foot or sqaure inch in a calculation means that the force is being exerted ON something. For example, lbs/sq. ft. might be used when talking about weight placed on a floor. The floor loading would be given in pounds per square foot.
Dennis-

p-51man

thanks!

CafeenMan

You lost your entire website and don't have a backup??? HOLY *#&$! They should be able to restore your files from a backup. My hosting only costs $7.00/month and I get a lot of space and bandwidth. I've got enough traffic now that I need to go to the next package. Maybe you should think about getting a real host and domain name. Also, start using that cd burner or zip drive or whatever. Man, I can't even imagine losing my entire site. That would make me suicidal.

EagleOne

CafeenMan

Yeah, it wasn't easy to cope with, but since I had no other way to face it, I sad let's write it all over again......It wasn't that bad actually because I was already planning on making some very deep changes on the site, so I would have to rewrite almost everything....This way I was forced to write everything....[]
Anyway, thanks a lot for the support.

The new website is partially up already, there are still some pages to be done and uploaded, but the main parts are already up. The article has moved to it's definitive location.

http://www.downwash.pop.com.br/articles/propt.htm

And the program I wrote can be found on the Software section.

Just to let you all know....

CafeenMan

I like your house.

Nice site. Looking forward to more articles. [sm=thumbup.gif]

EagleOne

I'm currently uploading some other programs and pages. But there's still a lot to be done......Oh well, let's go back to work.

BTW, so you liked my house?? I knew everyone I showed it would like. You can visit me anytime.....

CafeenMan

Well, I would come later today, but I'm having the oil changed in my 727, so it might be later in the week. Thanks for the invite though.

CheezeyPoof

You know, I have been flying for a few years now. Mostly "speed" types and I have asolutely no need to calculate this stuff. It gets you no where and your trying to find answers that don't work. I have seen a handful of pilots get so upset at there planes performance when the numbers don't add up. They waste most of there flying day fooling with this or that and they just don't get it! Its like trying to make 2 + 2 = 7.
These calculations produce nothing[&:]

CafeenMan

Some people like playing with numbers and even though the number might not reflect reality, they still give comparative results which can be useful. But I'm with you otherwise. I don't bother with it either.

EagleOne

CheezeyPoof ,

Everyone has the right to have an opinion.......

CafeenMan

I was seeing your site, and I have to agree with you, if I had a site like that and lost everything, I would be suicidal too.....Great site, nice work!!
Now I think I have lerned the lesson, I am burining evrything I have in CDs......Never is too much to backup all your data.

CafeenMan

EagleOne - I build my site on my computer and upload it. I don't work on my site in place. I have apache server installed so I can test before uploading.

I have my site backed up in three places on two hard drives, on cd, on ZIP disk and on another computer. I don't do it as often as I should, but if I lost something, the most I would have to go back is a couple weeks.

Thanks for the compliments.

- Paul

EagleOne

Paul,

I'm doing mine offline too in Frontpage. Right now, it's only backed up in a zip drive and in my HD. As soon as I finish what's left, I will burn it on a CD, safer that way. Maybe storing it in mom's computer too wouldn't be a bad idea......
So your site is super-safe, lots of diferent back-ups!!
Well, I think it's better to have as many backups as you can than having to write it all over again.....[]
I put a schedule to myself and I want to see if up until the end of this week I have what's left up and running. Next week at the most, since this week is gonna be a very busy one for me at school, and I may not be able to do everything, but I seem to always find time to do what I really want to (school stuff is not included ).