tag:blogger.com,1999:blog-5854741938955568545.post8999297718123633974..comments2019-01-16T13:36:10.052-08:00Comments on ElectricRCAircraftGuy.com--RC, Arduino, Programming, & Electronics: Propeller Static & Dynamic Thrust Calculation - Part 2 of 2 - How Did I Come Up With This Equation?Gabriel Stapleshttps://plus.google.com/105597643653053342490noreply@blogger.comBlogger36125tag:blogger.com,1999:blog-5854741938955568545.post-41825058263656661452018-11-13T02:35:23.492-08:002018-11-13T02:35:23.492-08:00This equation is applicable for multi rotors?This equation is applicable for multi rotors?Unknownhttps://www.blogger.com/profile/17361655634197128597noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-73760734987716128142018-09-24T18:26:23.318-07:002018-09-24T18:26:23.318-07:00Hi Gabriel,
Thanks so much for your work on produ...Hi Gabriel,<br /><br />Thanks so much for your work on producing this equation! It is a great piece of work, and it's very valuable for a class that I'm teaching. In your explanation, you found that your equation had the best fit to empirical data when the final term (d/3.296*pitch) was raised to a power of k2=1.5 (or 3/2), which you found to be an enigmatic result. I think I discovered why the value of 1.5 was the best value for k2. <br /><br />To understand this, let's break down your equation. The first term of your equation is expressed as: RPM * d^3.5 / pitch ^0.5. When you analyze the units associated with each variable, you get: Rev/min * in^3.5 / (in)^0.5. This can reduce to in^3/min, which is essentially a measure of the volume of air that is moving through the propellers per unit of time. When you multiply this value by the density of air (kg/m^3; after converting inches into meters), you can determine the total mass (in kg) moving through the propellers per unit of time. <br /><br />When you analyze the units from the second term of your equation, you get m/s (i.e., a velocity). <br /><br />When you multiply these two units together (after converting minutes into seconds), you get the following unit: kg*m/s^2, which you will recognize as an extremely important unit in physics (i.e., Newtons). Therefore, the only value of k2 that would yield a valid unit for Thrust (i.e, Newtons) is 1.5. Any other number would have yielded an invalid unit for this force. <br /><br />Please let me know if you agree and whether I'm missing something.<br /><br />Thanks again for your work!<br />JohnUnknownhttps://www.blogger.com/profile/05588172475842112412noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-39539547002642097642018-09-23T00:14:42.119-07:002018-09-23T00:14:42.119-07:00No reference book. It's my equation, hence the...No reference book. It's my equation, hence the title of this article: "How Did I Come Up With This Equation?" That title is intentional.Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-23996528730780306042018-09-22T22:49:29.777-07:002018-09-22T22:49:29.777-07:00what is the reference book of this equation?what is the reference book of this equation?knowledgehttps://www.blogger.com/profile/12882248972151492048noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-31391595748511846542018-08-21T10:06:01.711-07:002018-08-21T10:06:01.711-07:00Could you explain in more depth why increasing the...Could you explain in more depth why increasing the propeller diameter, increases the reynolds number and efficiency?Edward Granthamhttps://www.blogger.com/profile/14502841349070726504noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-23102473986182099132018-02-24T14:33:27.503-08:002018-02-24T14:33:27.503-08:00Sort of: I have not accounted for the inefficienci...Sort of: I have not accounted for the inefficiencies related to stacked propeller configurations, but perhaps if you considered a hovering X8 octocopter to have its top propellers in a static thrust condition (no forced inflow velocity) and the bottom propellers to be in a dynamic thrust condition (with inflow velocity induced by the top propellers) you could make the equations work for this case.<br />Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-15093803270981813812018-02-24T14:30:27.171-08:002018-02-24T14:30:27.171-08:00I don't account for any of that--which I'm...I don't account for any of that--which I'm pretty sure I even mention in one of these 2 related articles. This is a crude and generalized equation and considers somewhat of an empirical average of these characteristics, based on real experimental results of a variety of propellers. Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-37769913064389104942018-02-24T14:28:27.005-08:002018-02-24T14:28:27.005-08:00Yes.Yes.Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-91548382087815893792018-01-30T00:29:02.105-08:002018-01-30T00:29:02.105-08:00Hi Gabriel, will this eqn work for an X8 octicopte...Hi Gabriel, will this eqn work for an X8 octicopter configuration?Unknownhttps://www.blogger.com/profile/16214466124324465507noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-50428172722389836972018-01-06T19:36:56.749-08:002018-01-06T19:36:56.749-08:00Hello,
How can we calculate the F without knowing ...Hello,<br />How can we calculate the F without knowing the propeller efficiency...?<br />different brand props will have different geometry, aerofoil etc... Unknownhttps://www.blogger.com/profile/06760863362005073050noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-34061696055378573802017-11-27T10:15:55.933-08:002017-11-27T10:15:55.933-08:00can i use this equation to calculate propeller thr...can i use this equation to calculate propeller thrust of a quardcopter propellor Adarsh .R.Shttps://www.blogger.com/profile/09487761333996160699noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-22979427937309329122017-09-30T06:15:06.163-07:002017-09-30T06:15:06.163-07:00Clarification: when I say "tons of thrust whe...Clarification: when I say "tons of thrust when not moving" I mean "tons of thrust when the *plane* is not moving"--ie: tons of "static thrust." <br /><br />Also, I forgot to mention: I used that online sizing calculator I mentioned above on my <a href="http://www.electricrcaircraftguy.com/2016/05/battlebots-season-2-buzz-fire-drone.html" rel="nofollow">BattleBot flame-throwing hexacopter, "Buzz the fire drone"</a>, so I know it works. Plan to spend a good amount of time sizing things though. It's not easy.Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-32398941530563120722017-09-30T06:10:35.223-07:002017-09-30T06:10:35.223-07:00Vijay, this sounds like a university competition t...Vijay, this sounds like a university competition to carry as much weight as possible with <= 1kW power, and I'm guessing 21kg is the minimum required for an "A"? I'm sorry, I don't have the time to solve this problem for you. I do recommend, however, you use a good <a href="http://rcplanes.000webhostapp.com/calc_motor.htm" rel="nofollow">online sizing calculator like this one here</a>. Also, check out this video from FliteTest. I don't know what their power draw was but they carried 21.8kg for < $100 of parts. (<a href="https://www.flitetest.com/articles/flying-cinder-block/" rel="nofollow">Flite Test - Flying Cinder Block - PROJECT</a>) Now that's impressive! Keep in mind that you'll get better efficiency with high-voltage batteries (like 6S or higher), low kV motors, low RPMs, and large-diameter propellers. If you require more diameter but don't have the ground clearance, add more blades (at the sacrifice of efficiency)--ex: 3 instead of 2 blades. Just make sure that the power system produces enough *velocity* in the thrust that you can get the plane above stall speed. If you take what I said too far, for instance, you'll end up with a large propeller that produces tons of thrust when not moving and no thrust at velocity--meaning it will never get the plane above stall speed even though the static thrust is fantastic. This is because as you increase propeller diameter towards infinity static thrust will also approach infinity but induced air velocity will approach zero. Hmmm. Interesting...Best of luck!Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-64062142812484566222017-09-22T05:46:26.316-07:002017-09-22T05:46:26.316-07:00Please help me to find out motor propeller combina...Please help me to find out motor propeller combination for my 21kg plane which will running on 6s lipo pack and has to power less then 1000watt.<br />Please mail me on my below gmail if you have please..<br />24g.vijay@gmail.com<br />Vijay Goswamihttps://www.blogger.com/profile/01044561068737006006noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-26637253121637019712017-07-08T18:47:54.935-07:002017-07-08T18:47:54.935-07:00I'm guessing you removed your question because...I'm guessing you removed your question because you figured it out. At the end of the Expanded form of Equation 15, you have (d/(3.295*pitch)^1.5. No unit conversion from inches to meters is necessary for d or pitch because they both have the same units, so units cancel. Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-38109219242275312062017-07-06T22:10:38.623-07:002017-07-06T22:10:38.623-07:00This comment has been removed by the author.Borov Michaelhttps://www.blogger.com/profile/05839758042284354894noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-47834581075365347112017-06-28T18:43:39.538-07:002017-06-28T18:43:39.538-07:00Great question. Thanks for sharing NASA's thru...Great question. Thanks for sharing <a href="https://www.grc.nasa.gov/www/k-12/airplane/propth.html" rel="nofollow">NASA's thrust derivation based on Bernoulli's equation</a>. Whether you use Newton's equation like I did, or Bernoulli's equation, I've heard/probably even read somewhere in the past they are both equally valid, and if the same assumptions are used, should yield the same result. It's possible I've made some errors along the way, or different assumptions, but if you look at My Equation 5 it's actually surprisingly similar. I have V^2 - V^2 terms too. My Equation 5 says F = rho*A(Ve^2 - Ve*Vac), whereas the NASA equation has F = 0.5*rho*A(Ve^2 - Vac^2). Ve*Vac is very similar to Vac^2, but still different. Also, I go on to empirically correct my equation, whereas NASA simply left it as-is. Also, I don't require you have any idea what Ve <i>actually</i> is. Since it's very difficult to measure while flying, I just worked it right out of the equation so you could use the propeller constants and empirical correction constants instead of actually having to measure and know Ve. NASA doesn't take it that next step, so they expect you to know Ve, which isn't practical for most cases. <br /><br />I'll see if I can contact NASA and find the author of that page they have. Maybe he and I can talk about it.Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-63268451052885190862017-06-28T15:26:50.497-07:002017-06-28T15:26:50.497-07:00Very nice study, thanks a lot for your work.
Rega...Very nice study, thanks a lot for your work.<br /><br />Regarding the expression for dynamic thrust, it is slightly different to the one derived at https://www.grc.nasa.gov/www/k-12/airplane/propth.html using Bernoulli's equation. In particular, this equation has a (ve^2-vac^2) dependence rather than being linear with the aircraft speed. Looking at your plot of experimental data for dynamic thrust, the points look close to linear but slightly convex, which will be what one would expect from the Bernoulli's derivation. So it looks like something in between. Any thoughts about that?Francisco Rodriguezhttps://www.blogger.com/profile/02513192698079172727noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-65208856232705305672017-06-15T10:31:52.073-07:002017-06-15T10:31:52.073-07:00Hi I loved your article and found it incredibly he...Hi I loved your article and found it incredibly helpful.<br /><br />I'm looking for a way to convert from Thrust to Electric Power.<br />I understand it'll need additional variables I believe np(Prop Efficiency) and nelec (electric Efficiency)<br />are required but I can't seem to figure out how to do this conversion. :-(<br /><br />Do you have any recommendations or have you done this equation in the past?<br />Weston Losinskihttps://www.blogger.com/profile/15512181893590335302noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-58020861538773413932017-04-25T05:41:50.783-07:002017-04-25T05:41:50.783-07:00Hi, I can't think of anything to change other ...Hi, I can't think of anything to change other than density, but I really don't know how well the equation will work for water. Good luck and I'm glad you have found my site useful. Thanks for the gratitude!Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-13782543994746852012017-04-21T06:04:26.682-07:002017-04-21T06:04:26.682-07:00hi iam trying to build a big rov, and i cant find ...hi iam trying to build a big rov, and i cant find any reason to not use the equations you have deduced in this site (ill use water density instead of air).i want use this to find the right combination of thrust, propeller dimensions, rpm to decide right motors, propeller for the job.please let me know anything else should i change in your equation other than density. btw i am super impressed and fan of your site from now for the effort u have put in this, thanks on behalf of every hobbyist. Dheeraj Tippanihttps://www.blogger.com/profile/12664269013536587655noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-48200873851394779622016-11-14T08:10:30.586-08:002016-11-14T08:10:30.586-08:00It seems that some of the methodologies for choosi...It seems that some of the methodologies for choosing a power train for a given model start by estimating required and output engine wattage (assuming an engine efficiency) and maximum velocity, then use huge databases to choose a propeller. Is it practicable to develop a similar equation to your thrust equation to determine propeller input watts from diameter, pitch and RPM?Unknownhttps://www.blogger.com/profile/16000931283129545151noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-30542099334247278502016-10-06T01:57:55.032-07:002016-10-06T01:57:55.032-07:00Can we calculate for Thrust from a given value Tor...Can we calculate for Thrust from a given value Torque?choon lenhttps://www.blogger.com/profile/13147317877161408634noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-52669159791258245252016-09-25T15:09:58.999-07:002016-09-25T15:09:58.999-07:00Pitch has units of inches per revolution, diameter...Pitch has units of inches per revolution, diameter has units of inches, and RPM is a unit in and of itself: rotations per minute. If a propeller is listed as a 9x5 prop, for instance, 9 is the diameter in inches, and 5 is the pitch in inches forward movement per revolution. RPM is the rotational speed of the propeller in revolutions per minute. This can be obtained by testing the whole system, for example, and measuring the propeller RPM value with an optical tachometer, stroboscope, or electrical tachometer/oscilloscope reading the back EMF voltage readings across any one of the 3 motor windings and battery ground.Gabriel Stapleshttps://www.blogger.com/profile/10071071884455787806noreply@blogger.comtag:blogger.com,1999:blog-5854741938955568545.post-30147355299714326272016-09-24T02:56:57.381-07:002016-09-24T02:56:57.381-07:00Can you provide me with the units of pitch,diamete...Can you provide me with the units of pitch,diameter and rpm Deepak Singhhttps://www.blogger.com/profile/07670268771923993890noreply@blogger.com