Originally Written: 16 July 2013

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**In order to see a more detailed version of this article, and the most up-to-date version of this article as I make changes in the future, see its original posting location here: http://electricrcaircraftguy.blogspot.com/2013/09/propeller-static-dynamic-thrust-equation.html**

**Please rate this article after you read.**

**Propeller Thrust Equation, & Downloadable Excel Spreadsheet Thrust Calculator:**

**DOWNLOAD MY EXCEL SPREADSHEET THRUST CALCULATOR HERE (click link, then go to File --> Download)**

**Figures above: a preview of what is to come - Static Thrust (left) & Dynamic Thrust (right).**

I have been interested in propellers for a very long time. I've also been interested in how they produce thrust, and how forward velocity affects that thrust. Therefore, I've done a lot of thinking about it, and put a lot of time into understanding them better. Here is an equation that I came up with to quantify the thrust produced by propellers. I wanted it to be a simple approximation, with a minimal number of inputs. Therefore, it uses only the propeller's **pitch** and **diameter** (from the numbers on the front of the prop), and the **RPMs** at which the prop is spinning (this can be measured from a basic optical tachometer such as the one shown in the picture below). That's it!

**Here is the equation. **

The expanded form is shown to help you see where some of the numbers come from. The simplified form is shown you help you put the equation into a calculator or Excel spreadsheet easier.

**F **is static or dynamic thrust (it is called static thrust if V0 = 0), in units of newtons (N); **RPM** is propeller rotations per minute; **pitch** is propeller pitch, in inches; **d** is propeller diameter, in inches; and **V0** is the forward airspeed, freestream velocity, or inflow velocity (depending on what you want to call it), in m/s.

*If you want thrust in other units*: to convert newtons to grams, multiply newtons by 1000/9.81. To then convert grams to ounces, multiply grams by 0.035274. To convert ounces to pounds, divide ounces by 16.

Note: the equation has a hard-coded atmospheric density of 1.225kg/m^3, which is the "standard day" (avg. annual) density at sea level. Therefore, it will provide a thrust estimate assuming you are at sea level.

**Example:**

**DOWNLOAD MY EXCEL SPREADSHEET THRUST CALCULATOR HERE (click link, then go to File --> Download)**

Here is a thrust example, to demonstrate the use of the equation above: An airplane has a 10x6 propeller (10 in. diameter, 6 in. pitch), spinning at 10,600 RPMs when at full throttle on the bench. How much static thrust is it producing? Answer: using the equation above, the propeller is producing 1619g, 1.619kg, or 3.57lbs of static thrust. Download the spreadsheet above to change the values for your application.

At what airspeed will it produce zero thrust (ie: what is it's max thrust-producing airspeed)? Answer: ~60mph. Note: the 60mph is also the *pitch speed* of the propeller, which is an underestimate of the actual max thrust-producing airspeed, since I have not yet corrected the dynamic-thrust portion of the equation for the effects of things such as camber of the propeller and the unloading of the prop with increasing airspeed.

**How Accurate Is This Equation?**

**Short answer**:

*Static Thrust:*

It's a pretty good to decent ball-park estimate for all props, and a really good estimator for some props. For static thrust, consider it accurate to within +/- 26% for 95% of all cases. Slow Fly (SF) props are the least accurate, and usually produce much more static thrust than the equation estimates.

The plot below shows how well the equation approximates the thrust, when compared to actual, measured static thrust values:

*Dynamic Thrust:*

For dynamic thrust, consider the equation to be an underestimate of what the propeller is actually doing, by 15~30% when you extrapolate it out using the equation with the RPM value from a static test run. For extrapolating out dynamic thrust from a static test run, a good guess is that the actual zero-thrust airspeed will be around 15~30% higher than what the equation says. In other words, if the equation says you get zero thrust at 60mph, you might actually get zero thrust somewhere in the range of 69mph~78mph (60mph x 1.15 = 69mph, and 60 x 1.30 = 78mph). As I get more dynamic thrust data, I'll work on correcting this.

One dynamic thrust plot is shown below, comparing actual, measured values to calculated results from my equation above:

**For more details, more in-depth explanations, and additional figures, see the article at its original posting location here: http://electricrcaircraftguy.blogspot.com/2013/09/propeller-static-dynamic-thrust-equation.html. I will continue to update and improve the article on my blog as I gain additional insight and understanding in order to improve the equation.**

*Please help contribute your thrust data to this project, to help me improve the equation, by clicking here.*

I like the mixture of Metric and dark ages Imperial units that plague the aviation industry.

I would like to see the the air speed in Kilometers per hour as I don't come from one of those backward countries ;)

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If you email me I can give additional info too.

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My question is: What value should one use for velocity of air entering the inlet? Freestream velocity (zero, since the system is not moving) or the velocity of air entering the inlet (Volume flow rate divided by inlet area)?

Thanks!

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