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Old 03-11-2021, 08:25 PM   #1 (permalink)
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Default Blade Centrifugal Force and Kinetic Energy Calculator

First a disclaimer: You may be shaking your head and asking yourself: "Why make this silly calculator? Its a solution to a non-existing problem!" and you would be right. But it just so happens that I very much enjoy programming and building my own quality software tools, and this thing just sort of... emerged. That said...

Simple RC Heli Blade Centrifugal force and Kinetic Energy Calculator

I've developed a little JavaScript webapp that lets one solve for any unknown variable (given all the others), in the centrifugal force equation:

F = m * Rcg * ω * ω


F = Centrifugal force (N)
m = Blade mass (kg)
Rcg = Radius to blade CG (m)
ω = Blade rotation speed (rad/s)

Here it is on my server:

Blade Centrifugal Force and KE Calculator

Internally, the calculator implements the above equation using values stored in base S.I. units: (N, kg, m, rad/s), but externally, values can be entered and displayed using any desired units, (e.g. you can specify speed in fpm, kph, mph, m/s, ft/s, knot, Mach). Each text entry box also serves as a handy little units converter; when you enter just units with no number, the value is converted to those new units. The precision of each stored value is set to six significant digits.

In addition to the centrifugal force equation, this calculator also provides linear, rotational and total kinetic energy computations for the blade rotating about the mainshaft. The calculator allows you to specify a specific energy value and find the RPM that gets you there. The blade tip speed is also computed given the radius to the blade tip. There are ten equations used in all:

EQ1:    F = m * Rcg * ω * ω
EQ2:    vt = Rtip * ω
EQ3:    vb = Rcg * ω
EQ4:    KElin = m * vb * vb / 2
EQ5:    KElin = m * Rcg * Rcg * ω * ω / 2
EQ6:    KErot = I * ω * ω / 2
EQ7:    KEtot = KElin + KErot
EQ8:    KEtot = ( m * Rcg * Rcg + I ) * ω * ω / 2
EQ9:    I = m * l * l / 12 + m * Rcg * Rcg
EQ10:   l = 2 * (Rtip - Rcg)
The moment of inertia equation assumes the heli blade behaves as a thin rod (where Icg = 1/12 * m * l^2). The blade length l term assumes the blade has uniform weight distribution (which is not true if the blade has a tip weight). But this estimation for l is close enough, because the translation of axis term in EQ9 (m*Rcg^2), significantly outweighs the base thin-rod term (1/12*m*l^2) when the axis is translated to the heli main shaft.

This application is completely self contained and self documenting. All the necessary (free and Open Source) code is contained in the one (valid XHTML 1.0 Strict) text file: hfcalc.html (about 30KB). It needs no help from any external servers or libraries so can be conveniently used locally on your computing device when online or off. To get it, just go to my server by clicking on the link above. (But note that my server is just: "http:" and not "https:", so your browser may complain about security.)

Although I've triple checked everything, bugs (and blind spots) happen, so if anyone detects any problems, please let me know (so that I can fix it right up). And if any of you were to verify/validate/critique the accuracy of this implementation, I would be grateful - (in other words, please try to break it!)

Note that I work from an old desktop computer with keyboard and mouse only so I have no idea how this looks/behaves on a smart phone (I don't have one). If/As I add-to or refine this little ditty, I'll be sure to post here.

Here is what the initial release version looks like: (Note: default values are for an XK K110 running low headspeed.)

Hope some folks may find this useful!
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Old 03-11-2021, 09:09 PM   #2 (permalink)
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The core results are accurate enough for most people. There are problems with the kinetic energy calc just because of how you simplified mass distribution for example, but it is going to be within 20% or so for most configs, which is again, good enough for inquiring minds.

There seems to be some weirdness where if say you enter 16in for Rcg, and run the Compute F function, and then you change Rcg to something like 14”, it will just ignore that and revert to 16in. Probably better to throw an error for non-accepted units/notation.

Some units are incorrect. F is a force, so the resultant would be 100lbf, not 100lb.

Just a few suggestions if you want to extend the app without a bunch of effort. Several things are easy to calculate and are useful:
1. Ask for blade chord, and then output Reynolds Number for the blade perhaps over 5-10 stations along the radius.
2. For FF, allow input of airspeed, and then show local peak and min airspeed on the blade for advancing and retreating by station, with Reynolds number (extension of #1).
3. Include machine mass and blade count along with blade chord, to output disc and blade loading
4. Extending #3, output average flow velocity and mass flow at standard temp/pressure.
5. Extending #4, determine power required (a way to approximate rotor efficiency- not a great one since you are assuming all kinds of things in #4, but still- helps people to understand why rotor area has such a large impact on power absorbed.

It might also be fun to sort of put a simple reference chart for kinetic energy of a thrown blade at the hub, where for example you could post just say things people understand from the normal world- baseball at 90mph, AK47 round at the muzzle, etc just to let people better understand what sort of energy is in play with RPM and blade mass etc. Most people have no idea what 1000J means- even if they know the technical definition.
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Old 03-12-2021, 01:30 PM   #3 (permalink)
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Thank you for the helpful feedback and suggestions!

Yes, one of my motivations for this was to use it as a tool to possibly help educate/raise awareness on the very real dangers due to high energy associated with large helis/high headspeeds. When the subject comes up from newcomers, I have a real problem with many here recommending that new pilots: "go as big as you can afford". With the way the micros fly these days, (very well), there is a very strong (scientific) argument to be made that *ALL* new pilots should start on a micro - in the name of *SAFETY*.

Safety Engineering is all about energy. Energy does work and can do harm. If there is a lot of energy concentrated in one location, then that location is hazardous. A spinning rotor does not not look threatening - in fact, the blades disappear! But these things deserve a LOT of respect!

The small, lightweight K110 running low head speed represents the safe end of the RC CP heli spectrum. With only 1 J of energy per blade, crashes typically do zero harm to anything if TH is hit before impact. I hover mine indoors all the time (but don't crash much anymore).

Off to make a change or two...
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Old 03-12-2021, 02:47 PM   #4 (permalink)
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Default Updated: 20210312_1300

  • Improved error handling.
  • Additional units: lbm and lbf.
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Old 03-12-2021, 10:55 PM   #5 (permalink)
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Pretty cool. I have used other calculators before but having many of the most common calculations on one page is pretty cool.
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Old 06-09-2021, 11:21 AM   #6 (permalink)
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Default Corrected erroneous total energy calculation

It was pointed out to me on another forum that my total blade kinetic energy calculation was incorrect. I was erroneously adding the linear KE term (KElin) to the rotational KE term (KErot) to come up with the total KE (KEtot). It turns out that the second term in the KErot equation is the blade's linear KE so there was no need to add the KElin to get KEtot.

I've updated the calculator to eliminate the unneeded KElin, KEtot and vb parameters. Here's what the UI looks like now: (The default values now approximate the blade on the Blackbird DDWFTTW vehicle traveling at 50 mph.)

Once again, if anyone can see any errors/improvements on my calculator, please chime up.

BTW, while building this little app, I came across an excellent series of physics lectures presented by an MIT professor. This one in particular provided a very handy refresher in rotational kinetic energy. (His discussion of rotating neutron stars at the end was particularly mindblowing.)

8.01x - Lect 19 - Rotating Objects, Moment of Inertia, Rotational KE, Neutron Stars (41 min 0 sec)
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