Calculating Energy requirement for Rubber Powered, Spring powered and electric flight - RC Groups
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Aug 14, 2010, 06:25 AM
Design is everything.

Calculating Energy requirement for Rubber Powered, Spring powered and electric flight

I am trying to obtain information on the feasibility of spring powered flight.
( See Spring power for free flight in Free Flight forum)

In order to do this, I need to calculate power requirements. To simplify matters, the best is to calculate the energy needed for a five minute flight and make the comparison across the systems.

The following are available

For electric power : battery energy in mAh ( milli-ampere hours) , and voltage

For Rubber power : Propeller torque at maximum number of winds

For Spring power: Force x extension of the spring
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Aug 14, 2010, 07:17 AM
Grumpy old git.. Who me?
JetPlaneFlyer's Avatar
Calculating power required for level flight is quite easy:

Power = M.g.ld.v

W = Mass in Kg
g = gravitational acceleration (9.81m/s^2)
ld = lift to drag ratio or glide slope (so a 1:5 glide slope would be 0.2)
v = velocity in m/s

To relate input power, say from the battery on an electric model, to the power needed for flight then you also need to factor in the efficiency of the powertrain and critically of the prop.. these can add up to quite a low overall %.

So while it's wuite simple in principal the realisty is a bit more tricky.
Last edited by JetPlaneFlyer; Aug 14, 2010 at 08:03 AM.
Aug 14, 2010, 12:16 PM
Design is everything.
Thanks but what I want to do is arrive at a figure for work done which equals energy stored given only the values of the battery and the voltage it is producing to operate the motor. Assume 100% efficiency for calculation or maybe 60% efficiency it does not really matter -for comparison

How much work is done by a 800 mAh battery discharging over a period of 5 minutes?

How can you calculate the work by a rubber motor?
Aug 14, 2010, 12:39 PM
Grumpy old git.. Who me?
JetPlaneFlyer's Avatar
Originally Posted by knlever
How much work is done by a 800 mAh battery discharging over a period of 5 minutes?

How can you calculate the work by a rubber motor?
You correctly noted the answer to that one in your first reply.

One difficulty in the case of the spring and rubber is that force/torque is not contant so power varies considerably throughout the motor run.
Aug 14, 2010, 12:40 PM
ciurpita's Avatar


Originally Posted by knlever
Thanks but what I want to do is arrive at a figure for work done which equals energy stored given only the values of the battery and the voltage it is producing to operate the motor. Assume 100% efficiency for calculation or maybe 60% efficiency it does not really matter -for comparison

How much work is done by a 800 mAh battery discharging over a period of 5 minutes?

How can you calculate the work by a rubber motor?
Isn't work the application of a force over a distance. 1 Joule is 1 newton across 1 meter. A Watt is a Joule / second, and a Watt is also Volts times Amps. So an 800 mAh (miiilamp-hour) at 1volt (you didn't specify) is capable of producing 800 milli-Watts, or 800 milli-Joules/sec, for an hour,. Am I correct in saying that for 5 minutes, this is 240 (.8 * 5 minutes * 60 sec/min) Joules/Volt?

Could you do a similar analysis for the rubber band motor, determining the force applied per distance?
Aug 14, 2010, 02:48 PM
Registered User
Originally Posted by knlever
How much work is done by a 800 mAh battery discharging over a period of 5 minutes?
Work is irrelevant, it's the wrong term. You've already calculated the energy stored in a battery. That energy doesn't change whether you discharge it in 5 minutes or 10 hours. But if that amount of energy will fly a specific plane for 5 minutes then what more do you need to know ?

It doesn't matter if the energy comes from electricity, rubber, an IC engine or potentially a spring. If you have the same amount of potential energy stored in your spring as in the battery and you can work out a way to apply that energy as efficiently to power the same plane it will fly for 5 minutes again.

Aug 14, 2010, 06:58 PM
B for Bruce
BMatthews's Avatar
The battery pack is easy. You already know that it's 800mah's at X volts. Multiply the two together and you have watt-hours. Watt-hours converts to joules just fine.

To find the energy in a rubber motor you'd need to do a torque vs winds curve of a given motor and then integrate or "find the area under the curve". That area is then used to give you a value. But while I know there's something missing from this I have no idea what it is.... unless it's a matter of figuring out how much torque you can get back from it by using the revolutions over a given time? The math concept fails me at this point.

A spring is the same. It's the force used to compress or wind it (for a spiral clock style spring) over the inches of travel or revolutions. Then the same sort of conversion as the rubber motor would be required to find the total stored up joules of energy.

For rubber and springs I'd suggest you forget about anything like 5 minutes of powered flight. Only the biggest and best of the open class "dawn event" rubber models that hold near to 6 to 8 oz of rubber are capable of a 5 minute motor run with a useable power output to allow for lifting the rubber plus the size of plane that is needed to efficiently carry such a load.
Aug 14, 2010, 08:10 PM
Fanwriter - VAK Educator
Wendi Smol's Avatar

Energy, what energy?

Originally Posted by slipstick
..Work is irrelevant, it's the wrong term. You've already calculated the energy stored in a battery.

It doesn't matter if the energy comes from electricity, rubber, an IC engine or potentially a spring. If you have the same amount of potential energy stored in your spring as in the battery and you can work out a way to apply that energy as efficiently to power the same plane it will fly for 5 minutes again.
I can't see where he had stored the energy already in the battery??
And in your next but one sentence above you basically give the advise to work it out yourself (the original knlever).

One way to compare storage of energy is to find out how much can be put and retrieved in a certain mass of the store in question.

For example in 1 (one) kg of LiPo battery we can store 540,000 Joule or ca' 150 Wh. That is at the moment a good average of most manufacturers and includes everything like cable, packaging a.s.o.

A value for Methanol is around 20,200,000 Joule per kg.

So we now have to find a reasonable value for Rubber.

Rubber strips have been suggested as energy storage on the man powered "Sumpac" airplane: 2strips of 5/8" square and 15 feet long, which are about 1.265 kg.
Sumpacís consumption is ca' 400W, so for 3minutes we need around 72,000 Joule. This particular devise was designed by students of the College of Aeronautics Cranfield and also patented in 1961 or 62. Those data provide a value of caí 57,000 Joule per kg. Perhaps one could improve the numbers a bit, but they are so far from the LiPo figures that I think itís not worthwhile to pursue that road.
BTW any metal spring mechanics are even worse.

You see, there really is no choice.

Aug 14, 2010, 08:52 PM
Design is everything.
I think it is a good idea to use a specific model and work from there. Also, I am willing to go down on the flying time to one minute - outdoors it may be held aloft by air currents.

Is one minute flight time enough? It is certainly enough for me on CRRCSIM - use the power to gain height and do a few turns, then glide back down, doing a few aerobatics. It helps if the model is light.

So one minute enough for any of you ?

This system could be used for a low cost trainer model. Once the basics are learned on to batteries and longer times. But 20 minutes seems too much time really.

Let's decided on the size of the model first : it should use standard receiver and servos for low cost. There is no point in building a small model that uses expensive micro servos and a receiver - might as well buy a more expensive electric trainer.

Use a Guilows conversion - they fly with rubber power so that's a start.
Last edited by Designer2010; Aug 14, 2010 at 09:43 PM.
Aug 14, 2010, 11:24 PM
B for Bruce
BMatthews's Avatar
You may want to go and look at the rubber powered RC model that used an onboard camera. The thread is back in the Free Flight forum.

The model is lightly built from sticks and tissue and if you ask you'll likely find that it uses the smallest gear and battery for the airborne pack he could find. Even so without thermal aid the flights are only about 4 to 5 minutes long. And the motor he used was hellishly big by rubber model standards. He mentioned 32 strands of 1/4 wide rubber. I've seen grown men quake in their boots at the thought of only half that much rubber "blowing" when wound in the early post dawn open rubber models.

The prep work on the ground to stooge the model and wind it isn't the sort of thing that a newcomer to the hobby would tolerate. Also the fact that a broken motor is a certainty at some point and they would have to mess about with lubed rubber care and this is just a non starter of an idea. Rubber power for more advanced models such as an RC rubber model is and always will be a specialty part of the hobby. It's not the sort of thing that'll ever find it's way onto a store shelf as a flight trainer for newbies to the hobby.

The fellow hasn't mentioned the flying weight of the model but it's likely safe to say that it's in the 14 to 16 oz range. At that size and weight it would be so easy to fly that model with any number of small brushless motors. And the sort of battery pack that would provide the same climb and duration would be crazy small and light. In fact it's very safe to say that an electric motor, ESC AND battery back combo that would provide the same climb and easily three times the run duration as the rubber motor would be about 1/2 the weight or less than the rubber motor itself. Not to mention that it's far, far easier to obtain good quality electric flight components compared to a supply of good rubber that is suitable for model flying.

I know you have this dream of beating the odds but realistically what you want to do in terms of making an RC trainer or sport model powered by rubber or springs just isn't going to happen. The energy they can store just isn't the sort of thing that will fly a model for long or in a manner that most flyers expect.
Aug 15, 2010, 06:33 AM
Grumpy old git.. Who me?
JetPlaneFlyer's Avatar
Also the idea that rubber power is cheaper doesnít really hold up to scrutiny.

For RC you need a battery anyway just to power the RC gear. A battery that will power the motor AND the RC is hardly any more money.

ESC's and electric motors themselves are now very cheap, or a small glow engine is pretty cheap too.

Good rubber (and you would need good rubber) is not so cheap and for a largish RC model you would need LOTS of rubber. Rubber motors only last a limited number of uses before they start to 'nick' and eventually break so you need to replace the rubber motor at regular intervals. If you took a typical season of flying Iíd be pretty confident that rubber would probably cost more than a budget electric system.... And you would need a heavy duty winder, and have you checked the price of those lately?

Aug 15, 2010, 09:53 AM
Design is everything.
Seen the videos

I have seen the video of the rubber powered RC model that used an onboard camera.
I have also seen the other 'rubber powered rc flight' I appreciate all your comments, but I need to finish the calculations and wind this up (pun intended)

Example : Guillows 180 conversion

Take a look at this Guillows 180,

Uses a 2s 130 mAh pack, that is 260 mAh and flies for 5 minutes ( to be on the safe side). Plantranco lists it as 3.7 volts. So total energy for 5 minutes :

Energy = mAh x volts x time = 260mAh/1000 x 3.7volts x 2 x x 60seconds = 115.44 Joules

Also , w ork done = m x g x h . Therefore the energy provided by the battery is converted to potential energy of the model at height X metres above the earth

Potential energy = m x g x h = 56/1000 x 9.81 x height = 115.44 Joules. So height the model can be lifted by the battery assuming 100% efficiency = 209 metres (approx 600 ft)

Does this sound reasonable?

If it was Rubber Powered?

The model weights 2 ounces or 56 g. If it was powered by the standard Guillows rubber setup and weighed 56g with all the radio equipment inside - assuming the rubber motor will weigh as much as the electric motor and prop - how many minutes would it fly free flight?

Advantages of Rubber Power

I still see the following advantages of rubber powered flight for RC beginners

1. The plane and motor can be built and flown cheaply.
2. Crashes will not risk an expensive electric motor, esc and battery
3. Rubber power is environmentally friendly
4. A rubber motor + prop will cost less than a motor, battery, ESC, timer, and charger
5. Less build time

I have built a rubber motor powered plane - and it flies - easier to source supplies of prop and rubber motor than the prop and electric power.

If low cost makes it look like penny pinching, I can always use micro gear and make it very expensive!
Renewable energy is the future.
Last edited by Designer2010; Aug 15, 2010 at 10:15 AM.
Aug 15, 2010, 03:10 PM
B for Bruce
BMatthews's Avatar
He mentioned a 2S pack. So that's 3.7 x 2 = 7.4 volts. So the battery pack actually has twice the number of joules in it that you calculated.

Producing a 2 oz rubber powered version brings up some associated points. First off the airframe would need to be made a little stronger through the use of heavier fuselage longerons to withstand the tension and torque of the heavier rubber motor that would be used to match the weight of the motor, ESC and battery pack he's using. Plus you have to allow a portion of the motor, ESC and pack to go with the onboard RC gear to power it. So let's say we put 3/4 oz of rubber into the 2 oz model. That much rubber in that small a model will produce issues with prop size and torque reaction to where you would pretty much have to use a step up gear box. But gear boxes introduce their own troubles and definetly add some drag which would be a further waste of power. But let's ignore that for a moment and consider the flight of a 2 to 2.5 oz model with about 3/4 oz of rubber. I've flown rubber powered competition models that were a little larger than the Cessna, weighed about 2 to 2.5 oz and use about the same 3/4 oz of rubber we are considering here. The climb of these models is typically up to around 250 feet and the motor run is a whopping 25 to 30 seconds. Also any time that turbulence or a poor launch caused the model to produce anything resembling aerobatics the climb was cut to about half this amount. I've also flown some larger models that would be a likely candidate for adding a micro light RC control onto. These were old time Wakefield models where the model weight for that class was 8oz and the motor was about 3.5 oz of that total. Again the climb was not outlandish and the final altitude was about 300 feet following a 35'ish second motor run.

Let's look at the premium class of rubber model for another example. The early pre dawn open class models. These are all big light models of about 4 to 5 oz of structure powered with up to 5 or 6 oz of rubber. The fuselages are all crazy long to get the motor run to last longer. Obviously at the expense of torque. Even with this power to weight ratio and extreme size the motor run is only in the 90 second range. But to get the motor run to last that long the power is metered out very slowly through the use of huge 20 to 22 inch props that produce a strong climb for only the first 5 to7 seconds then it peters out to more of an uphill glide for most of the run time.

Or you can fold the motor over for a more powerful motor run. A buddy of mine had a Gollywock 36 inch model that would climb vertically up to about 250 feet before easing over to an angled climb and finally fold the prop for the glide. The performance was impressive to say the least. The energy density of the motor to model was more than 1:1. He had about 2.5 oz of rubber in the total 3.5 oz model. So climb it did and impressively so. But to achieve this even with all that rubber the motor run was LESS THAN 20 SECONDS. Also with the added weight it glided like a duck with a belly full of birdshot. No thermal meant no max for him. But the climb was the thing. Even if the prop was bigger to slow down the power burst the run time would still have only been up to around 30 to 35 seconds.

Something else to consider. A rubber motor, being a spring, is a torque device. In level flight or during a dive the prop unloads and increases the RPM of the prop to a great degree. This will allow a lot of turns and a lot of rubber torque to dissapate very quickly with little effective return. This would greatly reduce the energy available for more climbing. So rubber power has a low power density, lack of throttle ability and the effective waste of power in any flight mode other than the most efficient climb angle. This effectively limits rubber power to strictly a climb and glide style of flying.

And it's this run time, power dropoff and need to fly in a climb to most effectively convert the energy to altitude that is the issue. No one, other than us loony rubber flyer types, are going to be happy with that short a motor run. Let alone a run that only has "useable" power for the first 5 to 7 seconds and that demands that they only climb to altitude in order to have any hope of at least a 1 minute flight time. On the other hand electric power produces near to full power for up to 90% of the battery charge and they can carry a big enough battery pack to achieve 5 to 10 minutes of flying. And they can do this very easily by just plugging the packs into the handy charger and then unplug them and replug them into the model. No stooges to set up, messy oily lubed motors to insert into greasy lube smeared fuselages. No blast tubes that are needed to avoid a rubber explosion, no need to carefully inspect the used motors for nicks, no need to make up knot prone multi strand bulky motors and then to lube them with messy stuff. No need to spend as as much or more time winding the motor as the model will be in the air. No need to develop the skills needed to hold the strong tensioned fully wound motor while extracting the blast tube and installing the nose block on the winding hook.

Let's look at your perceived rubber power advantages;

1. The plane and motor can be built and flown cheaply.
- being RC controlled you're into the model right away for considerable money. Adding the currently VERY inexpensive motor, ESC and battery packs isn't that much more. And let's not forget that you need to buy GOOD rubber to power a model of the sort you are suggesting. A bag of rubber bands from the office supply place won't do it. Good flying rubber is about $20US a pound at the moment. And as JPF points out above a motor is only good for so many flights before the wear and tear weakens the rubber and edge tears make it far more prone to "blowing". If not provided for a blown motor will destroy the sort of lightly built model that is needed for rubber powered RC to be in any manner light enough to be considered successful. This brings with it the need for a sturdy stooge, blast tubes that need to be carefully placed and removed while supporting a wound motor. Again, these are skills and handling that few would want to bother with. VERY few in fact. Most would see us rubber flyers doing all this and then look over at the electric modeller that just plugs and flies and know exactly which they would choose. The very fact that you are so biased that you feel that rubber has a possible marketing niche just shows that you're very much a counter culture sort of guy. As such you fit into the free flight world with the rest of us just fine. From a personal point of view I commend you and would gladly shake your hand. But reality bites and the world would shun any attempt at a rubber powered RC model as much as they shun cooties as viable household pets.

2. Crashes will not risk an expensive electric motor, esc and battery
The nose blocks of rubber powered models sustain regular damage from crashes due to the required lightly built blocks and small guage wire prop shafts needed to keep the weight under control. Both rubber and electric are about equal on this issue.

3. Rubber power is environmentally friendly
Um... Depending on how electricity is produced in various parts of the world this may or may not be true. Also vulcanized rubber, which is what we are using in rubber models, isn't considered as environmentally friendly once the raw latex is vulcanized. Our rubber motors are technically as harmful as an old tire.

4. A rubber motor + prop will cost less than a motor, battery, ESC, timer, and charger.
At first this may seem true. But again keep in mind that rubber motors are only good for so many flights. Typically AND WITH CARE this is about 20 to 30 flights before the edges become nicked and torn and the motor needs to be replaced due to the greatly increased risk of explosive bursting while winding. A battery pack will easily provide the same number of flights over it's lifetime as anywhere from 5 to 10 boxes of rubber depending on the size of the model. At $20 a box you can do the math and see that electric actually wins handily on the rubber to battery cost comparison. And lets not forget that the ground equipment needed for a serious rubber model is not small or inexpensive either. A winding stooge is needed as well as a rather strong and heavy winding tool. And let's not forget the need for a blast tube. All of these items are mechanically complex, add up to a lot more volume of equipment to package and ship and to store at home and remember to take to the field. Overall I'd call it a wash for ground equipment for cost and a clear win for electric thanks to the simplicity of using the charger.

5. Less build time
-Definetly not. The need for a light but strong structure means that a rubber powered model of any sort has to be made from either lots of small parts and sticks if built at home from a kit. An electric model can be effectively built to the same size with a lot fewer all sheet parts thanks to the greater energy density of the battery pack.

And let's add on the freedom of flight that you get with the electric option. With the far greater energy density provided the flyer can perform multiple climbs instead of only one. That opens up the door to multiple touch and go landings. The easy use of throttle allows for doing aerobatics or just cruising around.

Do I need to go on with other advantages?

Rubber powered models are definetly fun. But fun only to the right people. You're obviously one of them just as I am. But don't let your enthusiasm blind you to the downside. Rubber flying can be very messy and the models require special care. The ground equipment is considerable and the flight times low unless passing thermals can be hooked. Half the fun is triumphing over all the limitations and producing a good flight. But there's few in the world that share this need to challenge themselves. Heck, the model industry has taken off since electrics became more practical, well performing and cheap. Back when we had to fly with glow engines the hobby was NEVER up to the numbers of casual consumer flyers that we have now. Electric power is what turned this around. Only a VERY SELECT few would take on the challenge of building and flying a rubber powered RC model. Look at how few there are even here in the forums at RC Groups. One? Two? And these are the dedicated modellers that would accept all the challenges and have the skills. The public? Nope, ain't gonna happen. They'll happily pay the extra and go electric.
Aug 15, 2010, 08:33 PM
Design is everything.
"B Matthews" thanks for your long and detailed analysis of the rubber powered RC scenario. I realize you are a very experienced modeler with lots of rubber powered time as well.

How do I respond- well yes, rubber power is only an interim step to building an electric model which will be my next step. For a long term flying experience, electric is the way to go, no question. But for experimentation in a limited space ( 20 m by 10 m ) the rubber powered models are fine.

I realize the limitations of rubber power - actually spring power is the ideal - that may not be practical as well, however I will continue my experiments in that area.

I am not sure you answered my question really, that is : take a look a this free flight rubber model:

captured Spitfire Harfang rubber powered model airplane (0 min 32 sec)

This is around a 30 second flight. If you add micro gear, and let fly it in a climb instead of a circle, might it not get a 1 minute flight ? Not sure how many turns he used to wind it though. Using a motor tube may help.

Here is the scenario: build the plane, fit the equipment and do a few flights maybe 10 or 20 to get the feel of RC flying. Then go on to electric flight. (Why would you want to do that? )

Basically it has to do with the efficient transfer of energy and the environment- let's just say I can't wait for the carbon nanotube spring battery to come into widespread use.

Capacitor powered planes are closer to my ideal, but I simply cannot get any over here for a reasonable price, nor the capacitors. See these planes

I think I should read that whole thread in detail.
Last edited by Designer2010; Aug 15, 2010 at 08:52 PM. Reason: corrections and ideas
Aug 16, 2010, 07:50 AM
Grumpy old git.. Who me?
JetPlaneFlyer's Avatar

Basing your design around any Guillows scale model is probably a bad place to start your project.
The Guillows scale models are very heavily built. If built to plan and using kit wood they tend to be too heavy to fly for long using rubber power. Getting 30 seconds duration would probably be doing well for most people. Adding even the lightest micro RC gear and all the necassary linkages and moving control surfaces would only go toward increasing the weight further, which would reduce duration, not increase it. I'd hazard a guess that 20 seconds or so would be all you could reasonably expect from a RC converted kit built Guillows scale model powered by rubber.....

You also said that the model should use standard RC gear including standard receiver and servos.. Well there is NO WAY you would get standard gear in a Guillows model and still be light enough for flight.

A larger non scale model would give you a much better prospect of success.. Something along the lines of the rubber powered RC model featured in the video posted earlier in the thread.

This type of project even if successful will never really appeal to the average RC flyer..The performance will be far too limited and the fuss of winding rubber motors and all the associated hassle would put almost all flyers off. 'RC rubber power' might appeal to a few freeflight rubber power enthusiasts who dont have big enough flying sites and/or are not fit enough to run after them any more.. that's about it.

Last edited by JetPlaneFlyer; Aug 16, 2010 at 07:57 AM.

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