Replies to This Discussion

Permalink Reply by Brad Hughey on June 18, 2012 at 8:03am

Coefficient of drag (Cd) is an attribute of an airfoil section (or any particular shape) at a particular angle of attack (AoA) and Re.  We can use calculus to integrate those values over the entire radius of the blade, but it appears to me your line of questioning is more along the lines of efficiency rather than Cd.  A holistic look at "drag" in this context really means "energy expended that is not added to thrust".  There are generally two ways of analyzing propeller efficiency: static (most useful for lifting propellers) and at some advance ratio (i.e. moving laterally - best for fixed wings).

I believe this prop has already been tested in a wind tunnel at the University of Illinois.  Perhaps you should start there.  They've already graphed propeller efficiencies vs. V/nD (advance ratio).  For static conditions, figure-of-merit or FM can be calculated by using their measured coefficients of power and thrust.  Here's the formula (in spreadsheet notation) which you'll need to use to calculate it from the "static" table data:  =((CT)^1.5)/(CP)*0.707))

University of Illinois Wind Tunnel Small Prop Test Database

• ▶ Reply

Permalink Reply by Tom on June 20, 2012 at 4:44am

Thank you Brad. The Illinois Database is really great, and probably exactly what I was looking for.

Actually, what I'm trying to achieve is to calculate thrust and drag of a particular (jDrones AC2830-358 + GEMFAN 10x4,5) engine + propeller system, to simulate roll, pitch and yaw torques. As there is no data for my setup available in Drive Calculator database, I thought to approximate it with EMP N2836/09 + EPP1045. But with the Illinois data I think I'll rather switch to EMP N2836/09 + AWS 10x4,7 (also available in Drive Calculator for drive efficiency calculation).

In the end, I'd like to simulate a system with current as input and thrust / torques as output. It seems pretty easy with thrust as all I need is a formula (already partly linearised):

thrust = Ct * rho * A * (omega * r) ^ 2

rho - air density, A - rotor blade area, omega - prop speed in rad/s, r - propeller radius

Roll / pitch torques also seem easy to calculate as:

pitch_torque = arm_length * (thrust_front - thrust_rear)

But I'm having problems with yaw torque. Is there a formula like the above that could relate propeller angular velocity to yaw torque?

• ▶ Reply

Permalink Reply by Brad Hughey on June 20, 2012 at 9:27am

Angular velocity is not enough to calculate torque.  Since you have power, just use that.  From classical mechanics (in imperial units):

Torque (lb/ft) = ((Watts*7.04)/RPM)

Use actual power, not ideal power of course.  Here's a good, practical treatise on the subject:

http://www.epi-eng.com/piston_engine_technology/power_and_torque.htm

• ▶ Reply

Permalink Reply by Tom on June 21, 2012 at 2:08am

Thanks again Brad, I'll read it through. From what I've seen already, it's going to make me understand imperial units better. How could anyone using decimal notation have invented it? :)

• ▶ Reply

Permalink Reply by Brad Hughey on June 21, 2012 at 4:21pm

Maybe the king of England at the time had big feet and a missing finger?  :-)

Anyhow, the best little conversion program I've ever found is free:

http://joshmadison.com/convert-for-windows/

• ▶ Reply

Permalink Reply by Tom on July 13, 2012 at 10:23am

I just read the UIUC paper (I'm unfortunately very busy these days) and was trying to use the data available in their database. But there is some ambiguity regarding part of the variables and units used. They say to have calculated the thrust coefficient, C_T, as:

C_T = T / (rho * n^2 * D^4)

but don't say what n or D is. I'm assuming n is RPM (or rad/s?) and D is propeller diameter (or radius?). How would you assume? What units shall I use for those quantities?

After consulting Drive Calculator I know, I should expect static thrust of around 700g at 6500RPM for APC 10x4,7, but cannot obtain such results with the formula above and C_T from UIUC.

I'm also guessing 1.2754 kg/m3 for air density, but maybe it's 0.0023769 slugs/ft3? I really wish the king of England hadn't had a missing finger.

• ▶ Reply

Permalink Reply by Tom on July 13, 2012 at 11:29am

OK. I've done some more calculations and assumed Mr Brandt and Selig were using Imperial units and as C_T is dimensionless, hence:

T [lbf], 1lbf = 4,48222N = 0,4535923kg

rho = 0,074887[lbm/ft^3]

n[rad/s]

D = 10inch = 10/12ft

Also noting that 1lbf = 32,174 [ft * lbm / s^2] I tried to obtain some sensible results for thrust assuming APC 10x4,7 propeller. I used the formula (eq. 5 from the paper):

T = C_T * rho * n^2 * D^4

which unfortunately leads to thrusts of 4000 times the magnitude expected (i.e. 4740kg for 6500RPM). Any clues?

• ▶ Reply

Permalink Reply by Brad Hughey on July 13, 2012 at 5:23pm

Just to keep the units consistent, I'm using feet, pounds, and slugs (standard density :: 0.00238).  You have the formula correct.

n = rotations per second (RPM/60).  So, for the APC 10 X 4.7 @ 6528 RPM:

T = (0.1274) * (0.00238) * (108.8)^2 * (0.833)^4 = 1.728 lbf (pound force)

That seems in the old ballpark to me.  :-)

Perhaps you used inches in the diameter?  10 inches = 0.833 feet.

• ▶ Reply

Permalink Reply by Tom on July 14, 2012 at 12:53am

Thanks, you just made my day. I made two mistakes: was not using slugs/ft3 for air density - but had tried this alone, and was using rad/s instead of RPS - and this was the main problem.

Attached the Excel file I did the calculations in and some characteristics below.

Attachments:

• APC_10x4,7_characteristics.xlsx, 18 KB

Permalink Reply by Tom on July 14, 2012 at 1:09am

Drive Calculator data for comparison below.