# Thrust to Speed?

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**1****Thrust to Speed?**

Is there a formula for thrust to velocity?

ie, I have a motor/prop which, when at full throttle, produces 720 grams of thrust, what is the speed which that air is moving?

Thanks

ie, I have a motor/prop which, when at full throttle, produces 720 grams of thrust, what is the speed which that air is moving?

Thanks

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**2**
Thrust can't be directly converted to speed.

A larger prop can produce that much at relatively slow speeds while a small prop will need lots of rpm and pitch speed to produce that much.

Working backwards with prop size you could probably estimate.

Try badcock.nets calculator and using your prop, play with the RPM until you get your thrust. Pitch speed should be close.

A larger prop can produce that much at relatively slow speeds while a small prop will need lots of rpm and pitch speed to produce that much.

Working backwards with prop size you could probably estimate.

Try badcock.nets calculator and using your prop, play with the RPM until you get your thrust. Pitch speed should be close.

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**3**Member

Join Date: Apr 2007

Location: Bristol, UK

Posts: 511

Strangely I was thinking about this just a couple of days ago. I cant see why you shouldn't be able to come up with a formula that gives a good estimate. I will have a go at working it out when I gat abit of spare time.

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**4**
mind you, I am in no way attempting to use grams of thrust to determine the speed of the end aircraft... but I can only imagine that so-and-so many grams of thrust must move at so-and-so speed regardless of rpm, volts, watts, prop and motor..

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**5**
Stink -- speed is determined by RPM and prop

Thrust is determined by RPM and prop

The above statements are very general, and there are other factors, but that's the easy way to look at it.

This is why smaller props, at high RPM, will push an airplane very fast, but have low thrust. Likewise, a 17x9 prop spinning slowly, will haul a Slow Stick straight up -- but not very fast.

Think of how a helicopter works: When a helicopter is hovering, the thrust is equal to the weight -- but there is NO SPEED.

There IS a formula to convert RPM into prop pitch speed, based on the prop pitch. If you are interested, I will be happy to share that formula with you.

Finally:

__pitch__.Thrust is determined by RPM and prop

__diameter__.The above statements are very general, and there are other factors, but that's the easy way to look at it.

This is why smaller props, at high RPM, will push an airplane very fast, but have low thrust. Likewise, a 17x9 prop spinning slowly, will haul a Slow Stick straight up -- but not very fast.

Think of how a helicopter works: When a helicopter is hovering, the thrust is equal to the weight -- but there is NO SPEED.

There IS a formula to convert RPM into prop pitch speed, based on the prop pitch. If you are interested, I will be happy to share that formula with you.

Finally:

- Think of THRUST as "low gear" -- like a tractor tread pulling a huge tractor through the mud, and over trees.
- Think of SPEED as "high gear" -- like a formula 1 racer, flying down the track. Think about how those same cars must be PUSHED out of the pits! (Because they are built for speed, not thrust!)

__really good__SPEED, or__really good__THRUST, or have a__just a fair__combination of both.
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**6**
To my understanding, in small flyers you usually want more speed, in large flyers you want more thrust in most cases.

Thrust is pretty much just the strength. If the motor has very little thrust, that's not good either, it needs to have enough strength to move the prop(s).

Thrust is pretty much just the strength. If the motor has very little thrust, that's not good either, it needs to have enough strength to move the prop(s).

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**7**I can show you a 10-ounce flat foamy, which is designed to "3-D hover", and has 15 ounces of thrust at full throttle -- but only 29 mph of prop pitch speed.

I can show you another 10-ounce flat foamy, which is designed to be a "parkjet". It uses twin ducted fans, and only delivers 6 ounces of thrust at full throttle -- but creates 49 mph of prop pitch speed. (Jet airframes want to travel fast!)

Remember -- the drag of the airframe increases EXPONENTIALLY, as the speed increases in a linear fashon. In other words, you need more thrust, the faster you want to go. You end up hitting a barrier at some point -- just after World War II, the barrier was the sound barrier. Now, the barrier is the speed of light.

Well, okay, the existing barrier is actually much lower than that, but it sounds cool...

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**8**Member

Join Date: Apr 2007

Location: Bristol, UK

Posts: 511

Ok, I think this is possible, I managed to put an almost working spreadsheet together at lunchtime. All you need to do is to go back to the equation F = MA where F = Thrust and M is worked out based on the volume of air passed through the prop x air density x pitch speed and A will be the pitch speed.

The trouble comes when working out the air volume passed through the prop because it is not the same as the prop diameter - you need to apply a correction factor which you can work out using test data (eg from a motor test).

You can then work back to get prop pitch and RPM based on thrust and prop diameter.

I'll put the spreadsheet and equation up on the web if I get the chance tomorrow.

The trouble comes when working out the air volume passed through the prop because it is not the same as the prop diameter - you need to apply a correction factor which you can work out using test data (eg from a motor test).

You can then work back to get prop pitch and RPM based on thrust and prop diameter.

I'll put the spreadsheet and equation up on the web if I get the chance tomorrow.

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**9**Ok, I think this is possible, I managed to put an almost working spreadsheet together at lunchtime. All you need to do is to go back to the equation F = MA where F = Thrust and M is worked out based on the volume of air passed through the prop x air density x pitch speed and A will be the pitch speed.

Also, I really don't see how you can use pitch speed (miles per hour) to calculate acceleration (feet per second, squared). That's like me telling you my car can go 120 mph at top speed -- what's my best acceleration?

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**10**Member

Join Date: Apr 2007

Location: Bristol, UK

Posts: 511

I look forward to understanding how you tackle calculating mass from the volume of air passed through the prop. I understand air has mass -- but what about altitude, temperature, humidity, etcetera?

Also, I really don't see how you can use pitch speed (miles per hour) to calculate acceleration (feet per second, squared). That's like me telling you my car can go 120 mph at top speed -- what's my best acceleration?

Also, I really don't see how you can use pitch speed (miles per hour) to calculate acceleration (feet per second, squared). That's like me telling you my car can go 120 mph at top speed -- what's my best acceleration?

You are right that to get an acurate result you must take into account altitude, temperature etc. Since we are only looking for an approximate value here I suggest that altitude and temerature (which ultimately effect air density) will be the dominant factors and we can ignore humidity.

Actually working out the the mass of air the prop moves will be very complicated. It should be possible to get a reasonably good aproximation using empirical data to derive a correction factor that can be applied to the prop diameter to take acount of the efficiency lost at the prop tips etc. Probably a different correction factor would be needed for different prop types and manufacturers but it should be easy enough to work out.

Once you have the effective area the prop works on it should be possible to work out the pitch speed needed to move the required mass to give the thrust (which we already know).

Of course all of this will only be relevant to working out pitch speed in the static test situation and wont tell you how fast the plane wil go.

*Last edited by Buck Rogers; 02-26-2008 at 11:30 AM.*

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**11**
A lot of work instead of using a tach I think.

Wouldn't figuring out air mass be much harder than figuring prop speed?

Using thrust and prop size shouldn't be too hard. A given prop will have to turn at a certain speed to produce a certain thrust.

Wouldn't figuring out air mass be much harder than figuring prop speed?

Using thrust and prop size shouldn't be too hard. A given prop will have to turn at a certain speed to produce a certain thrust.

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**13**Member

Join Date: Jan 2008

Posts: 23

Isnt thrust related to both pitch and prop size? I've always figured it was something like kxvxp where k is a constant, v is air flow through the prop, and p is the total area that the prop covers. I mean, two 90mm fans can put out different thrust figures despite being exactly the same fan, so air speed has to make a difference.

If there was such a formula, given prop diameter and thrust, one could feasibly find the speed out of the prop.

If there was such a formula, given prop diameter and thrust, one could feasibly find the speed out of the prop.

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**14**I might have failed in my word useage, so here in my attachment is what I am trying to figure out.

I have a little brushless attached to a small RTF model replacement prop which pumps out a screaming 720g of thrust.. or at least force on the scale.. I just want to know,

__not__how to produce that thrust (which I believe dives into the whole prop vs rpm vs everything) I am already at the thrust. just looking for the wind speed that is being produced.

I hope that made sense..

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**15**
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**19**
Exactly -- you have to figure what you time (and everyone's time on this thread) is worth, and compare that against the price of a wind speed meter.

With the wind speed meter, you get your answer -- no questions.

With this thread, you get a bunch of "maybe"s, and "unsure"s... :o

With the wind speed meter, you get your answer -- no questions.

With this thread, you get a bunch of "maybe"s, and "unsure"s... :o

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**20**Put that prop in a 10" diameter tube (if a 9" prop) and run it up. If its pitch speed is 25mph at the given RPM, then the air leaving the tube is = to the air entering. I believe the only way that number would change is if the air expanded on the back side of the prop. Creating a larger volume of air to be pushed out.

Thats somewhere to start. Knowing how much the prop unloads or flexes in use will affect the equation some but I'd have to wonder how precise you need this to be?

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**21**
I'm sure there are all kinds of vortices (eddie currents)...

Actually, I've got a new fog machine I'm supposed to receive very soon... Maybe I'll shoot fog into a spinning prop, and capture it on video...

Actually, I've got a new fog machine I'm supposed to receive very soon... Maybe I'll shoot fog into a spinning prop, and capture it on video...

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**23**New Member

Join Date: Mar 2008

Posts: 18

**Thrust, Revs and Horses**

There is a great and rigid formula expressing the connection between Thrust (static) Revolutions (dependent on propeller diameter and pitch) and Horsepower (generated by the engine at the crankshaft - glowplug or electric).

Unfortunately nobody knows what the formula is because there are too many practical variants like prop blade-width, section, thickness and helical geometry. This would be the Theory of Everything and it goes like this:

Start your elecric motor spinning and the more the volts, the higher the revs. Now stick a small diameter prop on the shaft and the motor slows down - but produces useful Thrust. If the prop is small the motor will only fly a small light model. Depending on the prop pitch it will fly that model at a certain airspeed called the 'Pitch Matched Airspeed' or somesuch and no faster,

Fit a prop with greater pitch and the model goes faster, up to the matched speed allowed by the pitch, again assuming a 'slippery' model.

But there comes a point when increasing the pitch has no further effect on speed as the model's aerodynamic shape, size, weight, finish and drag predominates and won't allow it to go any faster.

Pitch is everything - assuming your motor has the reserve of power.

Measuring static pitch (with the model tethered to a spring measuring- gauge) is not valid as the model has to speed up to its matched pitch speed.

However you can do a weird experiment here, a bit like in a wind tunnel in fact. Have your wheeled model on a table with the spring gauge hooked up to the tail and run the motor. Let's say it reads 100 grams of static thrust. Now direct an electric fan at the model head-on. Lo and behold, the model moves forward towards the fan, magically converting blow into suck!

You can now take the true dynamic thrust tmeasurement.

There is more if anybody is interested,

Harry Lime.

Unfortunately nobody knows what the formula is because there are too many practical variants like prop blade-width, section, thickness and helical geometry. This would be the Theory of Everything and it goes like this:

Start your elecric motor spinning and the more the volts, the higher the revs. Now stick a small diameter prop on the shaft and the motor slows down - but produces useful Thrust. If the prop is small the motor will only fly a small light model. Depending on the prop pitch it will fly that model at a certain airspeed called the 'Pitch Matched Airspeed' or somesuch and no faster,

*provided the model lets it.*This is the Crunch. In other words the model has to be light enough and streamlined enough to allow speed to build up to the potential speed dictated by the pitch__and no faster.__Fit a prop with greater pitch and the model goes faster, up to the matched speed allowed by the pitch, again assuming a 'slippery' model.

But there comes a point when increasing the pitch has no further effect on speed as the model's aerodynamic shape, size, weight, finish and drag predominates and won't allow it to go any faster.

Pitch is everything - assuming your motor has the reserve of power.

Measuring static pitch (with the model tethered to a spring measuring- gauge) is not valid as the model has to speed up to its matched pitch speed.

However you can do a weird experiment here, a bit like in a wind tunnel in fact. Have your wheeled model on a table with the spring gauge hooked up to the tail and run the motor. Let's say it reads 100 grams of static thrust. Now direct an electric fan at the model head-on. Lo and behold, the model moves forward towards the fan, magically converting blow into suck!

You can now take the true dynamic thrust tmeasurement.

There is more if anybody is interested,

Harry Lime.

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**24**However you can do a weird experiment here, a bit like in a wind tunnel in fact. Have your wheeled model on a table with the spring gauge hooked up to the tail and run the motor. Let's say it reads 100 grams of static thrust. Now direct an electric fan at the model head-on. Lo and behold, the model moves forward towards the fan, magically converting blow into suck!

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**25**I have to get clarification on this one.

Scott Stoops says "...lower pitch propellers create very high thrust at lower velocity, and higher pitch propellers create lower thrust but a much higher velocity."

That seems to contradict what you say above. Can you help us out here?

Thanks,

Frank