Having recently re-learned equations of lines, parabolas, etc. in my college algebra class. Also having acquired a 4 rotor RC helicopter and being frustrated with its very short battery life, I decided to try and find a formula that could help me understand the relationship between the battery and the flight time of the quad rotor helicopter. This way I could determine at what point there is diminishing returns based on the weight of the battery.

What I want to know:

What variables or inputs are required to understand this relationship?

What constants?

What is the formula?

Below is how I think I should approach this problem. I know a more finite equation with more variables for inputs exists (electric motor properties, energy management rules of the onboard computer, wind and atmosphere variables, flying style, half life of voltage output, "C" rating of the battery which defines maximum "burst" output of battery etc.). I am trying to keep it as simple as possible.

Variables:

Battery mAh (milli amp hours)

Battery weight (in grams)

Constant:

Weight of the helicopter (I think this is irrelevant)

max payload of the helipcopter

Desired output of the function: Flight time

Graph: X values are the ratio of mAh to weight of the battery or mAh/grams or milli amp hours per gram, Y values as flight time in seconds

Approach:

Add weight to the quad copter (grams) incrementally until the copter is not able to function (the point where it can achieve lift off but doesn't manuever very well or requires full throttle to maintain lift)

Using the existing battery (3.7v Li-Po at 500mAh) record the flight times for similar flight conditions and flight path. 15 samples sounds good.

From this get the average flight time for this battery (which weighs 12 grams and has 500mAh or 41.667 mAh per gram)

Use the relationship of time to mAh per gram to determine a formula that expresses the relationship between the flight time and mAh of the helicopter as such that the weight does not equal or exceed the maximum payload discovered in the previous test.

Graph the function to find the maximum value of Y, at the maximum value what is the X value?

Shop for batteries that do not equal or exceed the maximum payload and have a mAh/gram ratio that is close to the Y value maximum.

I found a battery that has 1250 mAh and weighs 23.5 grams giving it a mAh/gram ratio of 53.191.

Any thoughts and feedback on the approach or formula would be greatly appreciated. Also I hope this is the right forum to asks these types of questions.