Nov 04, 2017, 09:45 PM
Registered User
Data

# is prop thrust proportional to pitch?

Frequently cited in this forum is the idea that propeller thrust is directly proportional to pitch.

EQ. 1----T = K * rho*P*n^2*D^3

Propeller theory is well developed and verified and says that:

Eq. 2----T - Ct*rho*n^2*D^4.

For the first equation to be true it must equal the second equation.

EQ. 3----Then Ct = K*P/D

That is, Ct must be directly proportional to the ratio of P/D.

Static APC Thin Electric Ct data was extracted from the UIUC data base and augmented with data from other sources and the results plotted against P/D.
The value for Ct at P/D = 0.6 was selected and applied to the third equation to calculate the value of Ct for other values of P/D.

The results are shown in the attached graph. The conclusion is that thrust is not proportional to pitch except for low values of P/D.

Hence use of this formula for values of P/D greater than about 0.6 will likely produce results grossly in error, especially at P/D ratios approaching 1.0

### Images

 Nov 04, 2017, 11:34 PM Registered User Presumably you are discussing static thrust. Especially with the ridiculously high power to weight or static thrust to weight systems most LiPo powered brushless motor models have, IMO static thrust is of limited relevance, except in the negative sense that it overshadows the importance of available thrust at practical and desired flying speeds. While in flight thrust is practically impossible to measure in hobby situations, the combination of rules of thumb regarding power to weight and predicted pitch speed of at least 2.5 times stall speed, and much higher for high speed models is an effective proxy. Doesn't matter if static thrust is accurately predicted and measured to well exceed model weight if that thrust drops off so rapidly with forward speed that the model requires fill throttle to stagger around the circuit. Conversely, IMO it does not matter one jot if a commonly used formula badly predicts static thrust at higher P/D (probably because the blades are stalled at 0 airspeed) when at the common 100W /lb sports benchmark: whatever static thrust is developed is still way better than 0.5:1, ie more than ample for sparkling takeoff performance; Models require takeoff rolls of few to barely tens of metres; The prop unstalls either during the takeoff roll or shortly after and thrust likely is closer to predictions; The model can climb near vertically; and The model can achieve the desired speed. So for me, even if it is harder to model or predict, a higher P/D ratio than around 0.5-0.75 that seems to dominate commonly available (ie lhs, most online shops) prop sizes can be very valuable if not essential. I think that even after decades of electric flight, there is still a tendency to stick with the well undersquare prop sizes required for high rpm low prop diameter IC solutions, which are also affected by minimum thrust at idle rpm and landing airspeed, rather than larger diameter squarer props running at lower rpm. In my observation this is the case with some glow equivalent labeling brands which no doubt achieve good glow equivalence, but are often not an optimal clean sheet electric system solution. Although they are easy to sell to customers struggling with the breadth of options electric power offers.
 Nov 05, 2017, 12:13 PM Registered User Thread OP Scirocco, Your comments are good ones from a pragmatic view point. The purpose of this post was to encourage those who make the claim that thrust is proportional to pitch to include a qualifier to the effect that the equation is limited in its application. Without that qualifier one might be led to believe that high pitch props can produce far more thrust than they actually can at a given rpm and diameter. In any case, the rule fails completely as soon as the air speed is more than a few % of the tip speed which is most of the time in flight ( Advance ratio > 0.2). Its poor advice when people are mislead on these matters. Bill
Nov 05, 2017, 06:04 PM
Registered User
The data presented in the first post is rather abstract, so attached to this post are two graphs illustrating the effect of changing pitch while holding the diameter and rpm constant. The graphs plot 11 inch diameter thrust or prop input power as a function of air speed assuming 6,000 rpm. These results are based on wind tunnel data.

Look at the thrust graph at zero air speed - the static case. As the pitch increases from 5.5 to 7 the thrust increases almost in proportion, but as the pitch is increased to 10 inches the thrust hardly changes. It is not proportional to pitch at this level.

As airspeed increases the thrust starts to decrease, the fastest for the 5.5 inch case. The 10 inch thrust remains fairly constant for a while, then decreases to zero. The 7 inch case is intermediate in magnitude and change with airspeed. The form of these curves is typical for props having the same pitch/diameter ratios. They also show the value of high pitch props in achieving maximum airspeed.

Now examine the graph for power into the prop ( the output power supplied by the motor). Note that at zero airspeed the power increases with pitch more or less linearly between pitches of 5.5 and 7, then dramatically increases in going from 7 to 10 inches. The prop is now in full stall, no longer acting like an airfoil but more like a flat blade.

As the airspeed increases the 5.5 and 7 inch powers remain relatively flat, then decrease; the 5.5 inch faster than the 7 inch one. The 10 inch prop shows a relatively quick drop in power as the blades come out of stall, then flattens out before decreasing like the other pitches do.

There is no longer a linear relationship between pitch and thrust or power once air speed increases modestly. Hence the assumption that thrust and power are proportional to pitch is not true.

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 Nov 06, 2017, 07:15 AM Registered User I think the illustration assuming constant diameter and rpm is useful, because while a motor may unload in flight, it does not tend to speed up as much as an unloading glow engine. In effect, Kv x voltage (while the system is loaded) is a rev limiter. I don't disagree that this data set as presented shows that there is not a linear relationship between pitch and either thrust or power, but I do draw a bit different conclusion, because as per my earlier post I am not overly interested in static thrust - I focus on thrust at flyable speeds knowing that available static thrust is already overkill. Pitch is going from 5.5 to 7 to 10" ie factors of 1.27 and 1.42. At 40 km/h, I see thrust increasing from 300 to 600 to 760g, factors of 2 and 1.27. At 60km/h the 5.5" prop is no longer useful, but from 7" to 10", thrust increases from 300 to 560g, a factor of 1.86. My conclusion is that for airspeeds greater than say 2/3 of the pitch speed of a lower pitched prop, a higher pitched prop at the same rpm yields a disproportionately greater increase in thrust, ie a lot better than the 'thrust proportional to pitch' model, while at lower but flyable speeds (talking fixed wing non stalled models here) the thrust delta may not be as big as expected - but importantly thrust is still always higher. Power consumed is the price paid for the thrust, and again I agree this data set shows power consumed higher than a power proportional to pitch model. However, given we tend to set our power systems up to cope with the power demands of the static full throttle case, the system is well able to deliver the required power, albeit at the price of duration if that power is to be sustained - which is not that often unless in competition settings. Another conclusion is that increasing pitch in the increments readily available can be a more granular way to improve thrust without the big step changes in power required involved in increasing diameter, especially if P/D is kept constant in an attempt to not lose too much pitch speed at the higher load/lower rpm - of the order of D^5 as you stated in a different thread. My point here is that even if you get less thrust increase (at lower airspeeds) or more (at higher airspeeds) than proportional to the pitch increase - you do get more at all flyable airspeeds, and if that's a factor, higher available speeds. Speed isn't everything of course. I've only participated in one well measured specific thrust testing experiment, but the improvement in specific thrust for a higher P/D prop (14x12 vs 14x8) was significant at relatively low cruise power settings, as shown by longer duration (about an hour) flying at the same autopilot controlled airspeeds for the same energy consumed. Encouragingly, the improved specific thrust was pretty well predicted by Ecalc. ps - I'd be interested to see the curves for fixed diameter different pitch at a more realistic 9-10000 rpm which would greatly expand the speed range - but I guess that would have required a higher speed wind tunnel. pps - I come from a background of flying constant rpm fixed diameter turboprops, so every power change is a function of varying blade angle/pitch. I sometimes wish for variable pitch model power systems (that are not helicopters) and then the reality of cost and complexity vs relatively small cost and weight penalties for oversized fixed pitch systems hits.
Nov 06, 2017, 10:16 AM
Registered User
Attached are graphs of thrust and power for 11 inch props running at 10,000 rpm. The thrust increases as n^2, the power as n^3 and the thrust zero crossing increases as n^1 for both.

The wind tunnel experiments were run to examine the effects of low speed operation on model props, specifically looking at the effects of Reynolds Number. As the rpm increased at a given advance ratio, the prop efficiency also increased, but at a slower and slower rate. Most of the tests for props of 11 inches were limited to rpm of 6,000 or less as the change was small above 6,000 rpm. My program model uses the 6,000 rpm results as they are more indicative of normal model operation than the lower rpm cases.

Increasing the rpm beyond 6,000 probably under estimates the actual values by a small amount.

### Images

Last edited by aeromodel03; Nov 06, 2017 at 10:25 AM. Reason: errors
 Nov 28, 2017, 01:00 AM Registered User For the sake of simplicity; a static ground test and flying are two entirely different realms for propellers. A helicopter with an engine driving a low pitch big rotor has enough thrust to lift itself up; install that same engine in and airplane pointed straight up and it ain't going to leave the ground. But go into level flight and no way can the copter keep up with the plane. A rule of thumb from the control line flying era......experiment with prop diameter and pitches until you find the one that makes a speed plane go the fastest and you will discover that the speed is actually about 10% faster than the RPM and pitch calculate. A lot has to do with compressibility and stalling at critical tip speeds and pitch vs airspeed.
Nov 28, 2017, 04:24 PM
Registered User
Quote:
 Originally Posted by Jim Petro A rule of thumb from the control line flying era......experiment with prop diameter and pitches until you find the one that makes a speed plane go the fastest and you will discover that the speed is actually about 10% faster than the RPM and pitch calculate. A lot has to do with compressibility and stalling at critical tip speeds and pitch vs airspeed.
The reason is related to the way that pitch is defined physically. It is defined relative to the chord line which extends from the extreme leading edge point to the extreme trailing edge point. The angle of attack, when the forward airspeed and the rotational airspeed make the incident angle zero at the chord line, is not zero, but about 3 to 5 degrees greater. Hence the zero thrust condition occurs at about 10- 12 % greater forward airspeed.
Bill
 Jan 27, 2018, 04:31 AM homo ludens modellisticus Check out the simplified link guys Motorcurrent is proportional to pitch¹ (simplified), voltage², Kv³ and diameter⁴. Power drawn is proportional to pitch¹, voltage³, Kv³ and diameter⁴. Vriendelijke groeten Ron
 Jan 27, 2018, 05:42 AM Youtube channel : solentlifeuk eCalc does a good job of producing thrust vs rpm graph ... scroll down the page after pressing calculate. "Doesn't matter if static thrust is accurately predicted and measured to well exceed model weight if that thrust drops off so rapidly with forward speed that the model requires fill throttle to stagger around the circuit. " ....... this is the pitch argument .... you can have a large diameter with low pitch producing massive thrust - but the nett thrust to accelerate the body falls of quickly as the body speeds up. It reaches max speed at low figure and nett thrust becomes zero. Its the service boat vs Speedboat situation .. where both have same power, can have same rpm ... same thrust but service boat reaches max prop speed much earlier. The service boat like the low pitch plane prop has tremendous pulling power though and very little stall characteristic when under serious load trying to pull a body. Nigel Latest blog entry: Lack of budget gear now .........
Feb 05, 2019, 05:20 AM
Entropy is happening!

# A little off topic........

Apologies.......up front.
Can someone direct me to a propeller speed chart?
I read the term "prop speed", but have yet to find information on this.
Feb 05, 2019, 05:46 AM
Quote:
 Originally Posted by Jim.Thompson Apologies.......up front. Can someone direct me to a propeller speed chart? I read the term "prop speed", but have yet to find information on this.
That's like asking how long is a piece of rope ...

Programs like eCalc allow you to enter motor / battery / prop .... you get speed / thrust results out.

You can in fact calculate theoretical speed ...

Pitch is the distance a prop will move forward in one rotation. Therefore you multiply up against RPM to get speed. But that is theoretical and faster than actually realised in practice.
Feb 05, 2019, 02:11 PM
Entropy is happening!
Quote:
 Originally Posted by solentlife .............................. You can in fact calculate theoretical speed ... Pitch is the distance a prop will move forward in one rotation. Therefore you multiply up against RPM to get speed. But that is theoretical and faster than actually realised in practice.
Of course! Thanks for that. I am sometimes blind to the simplest things..................
Feb 05, 2019, 02:52 PM
Quote:
 Originally Posted by Jim.Thompson Of course! Thanks for that. I am sometimes blind to the simplest things..................
Here's a spreadsheet I knocked up ages ago to help me with my Need for Speed designs ... it has you'll notice input to allow calculation of actual factor vs theoretical.

Please note - it is not providing real life solutions ... but can help to provide a starting point for tests.