# Thread: Formula For Flight Time of RC Helicopter - FUN!

1. 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)

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.

2. Not my field, but you are searching for the battery that has the longest lasting power for its weight I guess? This depends on how the heli is constructed and what can physically fit in it. The weight of the copter certaintly would not seem irrelevant though as the heavier it is the more battery juice yolu will need. You already know this though or you would not be concerned with the battery's weight verses how much (milli)amps it can deliver and for how long. What type of battery did it come with?

3. I have yet to weigh the helicopter, but its weight will be constant less the battery, so what it weighs doesn't fit into the formula (I think). The shape of the battery and whether it fits or not is irrelevant as well because if the battery that gives the best flight time doesn't fit the current chassis, I will make it fit

For more details:
Helicopter being used - Skyrocket Toys: Sky Viper Camera Drone Quadcopter
Existing battery: 15C 3.7v 500mah lipo battery 751855 rc helicopter battery for tools soler light ups light weighs approx 12grams, 500 mAh

4. Always integrate. The area under the power usage (y axis) versus time (x axis) curve is energy consumed.
The current and voltage must be measured in real time (sampling is fine), the measurements are processed (some type of DA module with maths ability) and a user friendly output is created (screen, gauges, print out).
Cars do this all the time now.

Mark Twain is said to have a written a letter in which the PS was " I'm sorry, I did not have time to write a shorter letter."

Clarity is lost when posts, articles and speeches are long. The message is lost, people change the channel.
Completeness at the expense of clarity is the sin of many speeches and posts.

5. "Always integrate. The area under the power usage (y axis) versus time (x axis) curve is energy consumed.
The current and voltage must be measured in real time (sampling is fine), the measurements are processed (some type of DA module with maths ability) and a user friendly output is created (screen, gauges, print out).
Cars do this all the time now."

How would measuring the voltage and current real time help me determine the correct mAh to weight ratio for longest flight time? Or are you saying the approach of using mAh/weight flawed in the first place?

These types of batteries all have a very similar "curve" for their output. They always start at 4.2 volts with a full charge and drop below 3.7 volts after their expended. How long they last is determined by mAh. Generally the larger the mAh the longer you can fly your RC helicopter. However, the higher mAh generally the more weight. So at some point the extra weight of the battery causes the operator of the helicopter to remain at full throttle to maintain lift, thus reducing your flight time. Its also possible the battery will weigh to much for the helicopter to take flight.

6. Hello,
We sometimes get great problems like the one you pose, where a real situation, with real limitations of the equipment are brought up.
The battery weight is a significant part of the total weight of the RC helicopter system. A completely different world than an electric fishing motor.

I am not an aviation expert. I cannot help you as an enginner but as a manager I would do the following phone the RC manufacture with a convincing story to help me out.

You could for example tell him you are the president of an RC club doing a big project with an Ivy League school , tell them how their stuff is great and used by all your members, butter him or her up, ask the customer service person to put you into contact a good contact to answer a flight autonomy question of their equipment. Very quickly a guy like you will be able to tell if he is the correct person to answer, if he is great, if not you must politely get to someone else.

Otherwise I would do an experiment with different sized batteries. Large mass and highest energy density. Small mass and highest energy density. I was thinking of doing the same thing with lower energy batteries and the same large and small mass but perhaps this would be almost be the same as not fully charged (eg 50% charged) high density batteries.

Very interesting situation.

Reminds be of a scuba diving test I did decades ago. You throw your equipment into a deep pool. You then dive in with only your bathing suit on, you swim to the bottom, stay on the bottom, put on all your equipment on the bottom, come back with your all your equipment (fins, mask, tank, weights) on, your mask cleared of water and you are breathing thru the functioning regulator.
This is also done with your fins, snorkel and mask dumped in the bottom. No weights, heavy tank and air to help you down there.
The dilema is the bigger breath you take and the more buoyant you are and the harder you must swim to stay on the bottom.

7. pikpobedy,

I love the scuba example! I contacted the manufacturer a while back and asked if their engineers had put thought into the battery weight and flight time. The rep said he would contact their engineers but never got a response. Then I told him about my plan to experiment with different batteries and he wanted to know what my findings were!

The best batteries out there are Lithium Polymer (Li-Po). They way the least.

Thanks for the feedback!

8.

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