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Old 03-11-2021, 08:25 PM   #1 (permalink)
ridge-runner
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Join Date: Jul 2012
Location: Austin, UT USA
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

Where:

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:

Code:
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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