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Magic numbers for modelers...

Old 11-19-2007, 08:52 PM
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info Magic numbers for modelers...

No blog on Wattflyer, so let's post this article here. Hope it will help someone...

Magic numbers for modelers...

Schoolboys (and girls) know Watts, Ohms and Amperes. Modelers speak of props, lipos and BESC's. Not to forget the mysterious KV and the famous C, which is not the speed of light... But what hides behind these cabbalistic concepts? And how do they relate to the everyday business of flying RC machines? Follow the magic numbers...

Today's pilots understand that you get more from a good electric setup than an average IC engine. Cheap sources of equipment have dramatically changed the price tag on brushless motors, ESC's and batteries. But it is still something akin to the dark arts to select the right combination of these three items in order to fly well. The best way to success is to follow the secret recipe of electrical gurus, based on kilometers of burned windings, and the third law of universal common sense. Enter the hidden side of real-life quantum physics, the one that mixes weight and mass, translates temperature in 'seconds-of-finger-on-the-motor-bell' and flying times in burned amperes... Who cares for the Science, as long as we can punch holes in the sky

Buy your watts by the kilo (or Pound)
The first magical number tells you how much watts you need to fly your plane. Of course, it works only for decently matched systems. A GWS parkflyer won't fly with a 300gr motor,
however powerful it is...

Foamie, motorglider, Piper Cub: 100watt per kilogram (2lbs)
Trainer: 150 watts per kilo
Warbird, 'sport' aerobat: 200 watts per kilo
Racer, 3D: 300 watts per kilo
EDF Jet: 400 watts per kilo

Examples: a 3kg (6lbs) 150cm (60") Hurricane will fly on a 600watts setup. A 2.5kg Calmato will require 375 watts, etc.

Watt is pushing us forward?
The second magical number gives an idea of how much static thrust you can expect from a good setup. Once again, this is only true for a propulsion system that is performing normally.
These values give a good indication of what is possible... and what is not.

Brushless outrunner: 4gr per watt
EDF: 2gr per watt
Brushless 'inline': 2gr per watt
Brushless 'inline' with gearbox: 5gr per watt

Examples: A warbird with a 1000 watt brushless outrunner will have 4kg static thrust. An EDF jet having a 600 watts power system gives 1200gr thrust on the ground.

Powerful horses...
The third magic number is in fact a magic formula, one that most of us forgot after school...

Watts = Volts x Amperes
Volts = Watts / Amperes
Amperes = Watts / Volts

How does that relate to horses? Easy: you can convert watts to horsepower with the following rule: 1000 watts = 1.34 HP or 1HP = 750 watts.
Example: a Trainer aircraft with a 12 volt battery delivering 40Amps gives 480 watts (or 0.65HP). Note that the same plane having the same performance in IC would use a .40ci engine providing 1HP, which is 750watts... This is because electrics have a better efficiency, with more power at lower rpms. A similar phenomenon applies to diesel vs. petrol cars. The diesel drives better even if both cars have the same 95HP.

One Hot Minute!
E=Mc2 and the planet is warming up, everyone knows that. Electric motors also get warm. To know how much too warm the windings should not glow, here is a rule of thumb that is nothing short of magical...

Prop aircraft: motor weight in grams x 3 = max. watts.
EDF: motor weight in grams x 5 = max. watts.

Example: a 235gr brushless outrunner can dissipate 705 watts for a minute without meltdown.
A 200gr inrunner on an EDF will not die even at 1000watts.
Of course, this is assuming the motor is correctly used and cooled by adequate airflow.
This rule is only true for brushless motors. Old 'can-style' brushed motors like the Speed 600 don't survive more than their weight in watts...

Resistance is useless...
Gold is a fantastic metal when it comes to moving currents. Unfortunately it is also very heavy. That is the main reason for us to use copper in electrical wires. But then copper transforms some of the current into heat. Not only does it fuel global warming, but it reduces the available in-flight power, which is a real catastrophe!
To avoid this dramatic event, one should always use large enough wires:

Up to 25A: 1.5mm wire section (15 AWG)
Up to 60A: 2.5mm wire section (13 AWG)
Up to 100A: 4mm wire section (11AWG)

Not only wires, but connectors and soldering must be able to handle the current. In this field like in others, bigger is also better...

Round and round
You always wanted to know what the famous 'KV' stands for? This indicates the number of revolutions per volt provided by an electrical motor. It gives us the 'nominal' rpm of a motor on a plane.

rpm = KV x volts x 3/4

Examples: a 1200KV brushless outrunner connected to a 10 volts source will turn at 9000rpm. A 4200KV inrunner on 10 volts will spin at 31500rpm.

Full or empty, that is the question...
The voltage of NiMh cells is said to be 1.2 volts and lipos are sold for 3.7 volts. These 'nominal' values are confusing at best. The real figures depend on what you need. For instance, to know the wattage of a power system, you need to take into account the voltage of the battery at full throttle. But when you need to know if a battery is full, you measure the 'idle' voltage. The values written here give you an idea of typical 'real life' cell voltage.

Lipo in flight (motor full power): 3,3 volts
Lipo fully charged (idle): 4.1 volts
Lipo empty (idle): 3.7 volts

NiMh in flight (motor full power): 1.1 volts
NiMh fully charged (idle): 1.4 volts
NiMh empty (idle): 1.2 volts

Example: In order to get 300watts from a power system, you will need a 3-cell LiPo or a 9-cell NiMh battery and a motor loaded to about 30A.
Here are the (rounded) 'in flight' voltages of typical lipos:
2S = 7 volts, 3S = 10 volts, 4S = 13 volts, 6S = 20 volts, 10S = 33 volts.

Need for speed? Get some serious pitch!
Chosing a prop is not easy. Most people select the right diameter so that the motor doesn't soak too much current . But the pich is often disregarded. Nothing replaces the test flight, but here are some magic numbers to guide you when choosing the pitch of a prop.

Airspeed in kph = pitch (in inches) x rpm / 800
Airspeed in kph = pitch (in cm) x rpm / 2.000

Example: On a big trainer aircraft, a large 14x4" prop spinning at 8000 rpm will get you 40 kph of speed, which is marginal.But a 11x8" at 11000 rpm gives 110 kph which you don't need. The best choice will probably be a 13x6" spinning at 9600 rpm and providing a top speed of 72 kph. This is true for all planes, not only electrics.

Masters of the 'C'
The label on your brand new lipos reads '15-20C', but there is also a '1C' somewhere else on the sticker... WTH???
The '1C' in small letters means the maximum charge current is 1 time the cell's capacity (all lipos charge at '1C'). On the other hand, the '15-20C' note promises you can discharge the battery at 15 times the capacity and even push it briefly to 20 times the capacity without damage. The truth is that most manufacturers are too optimistic, so forget the second number and try to keep the 'peak' discharge current under the first number. A 'realistic' discharge current can be calculated like this:

Max discharge current on the ground = (first number) C x capacity / 1250
Max discharge current during 1 minute = (first number) C x capacity / 1500
Max continuous discharge = (first number) C x capacity / 2000

Example: A 3000mah '20/30C' battery should be able to discharge at 60A during a few seconds. It will survive a take-off at 48A. A whole flight alternating slow passes and full throttle at 40A will be OK. And it could be discharged at 30A continuous without degrading.
Whatever the 'C', remember to provide adequate airflow to cool the battery.

The heat is on!
To cool down an IC engine, you just cut some holes in the motor cowl. For an electric aircraft, you also have to provide cooling for the ESC and batteries. The warm air has to find it's way out of the plane so there have to be additional holes at the rear... But what size of holes do you need to drill?

Air entry surface (cm) = number of watts / 40
Air exit surface (cm) = number of watts / 30

Example: a warbird using 1000 watts needs 1000 / 40 = 25cm of cooling air intake and 33cm of opening behind the battery to let the warm air exit. The exit MUST be larger than the entry to avoid warm air stagnation which is even worse than too small an air intake.

Check the internal resistance
Modern batteries provide tremendous performance thanks to a very low internal resistance ('Ri'). But all batteries are not equal. To compare two brands or to know if an older pack is still fit-to-fly, you must measure the Ri. All you need is a voltmeter and an (cl)amp meter (or a wattmeter that combines both functions).

Measure the voltage 'V1' during a discharge at a current 'A1' corresponding to 1C
Measure the voltage 'V2' during a discharge at a current 'A2' corresponding to 10C

Ri = (V1 - V2) / (A2 - A1)

Example: on a brand new 3-cell 2200mAh lipo you measure 11.4 volts at 2.2A discharge and 10.5 volts at 22A discharge. The Ri of the pack is (11.4 - 10.5) / (22 - 2.2) = 0.045Ω. This means a single cell Ri of 0.015Ω.
Several month later, your plane doesn't fly like it used to do. You measure Ri again with 11.2 volts at 2.2A and 9.5 volts at 22A, which gives 0,086Ω. This means that the battery has lost half its performance...
To be meaningful, Ri must be measured in 'standard' conditions. Ambient temperature, cells temperature and state of discharge have a direct impact on the results. The easiest is to always measure Ri on a freshly charged pack at ambient temp.

What goes up...
...Must come down. But when? Follow these magic formulas to estimate how long you can fly using a specific battery:

Contest or 'full throttle': Seconds = capacity (mAh) x 4.2 / max current on the ground
Aerobatics: Seconds = capacity (mAh) x 7 / max current on the ground
'No-stress' flight: Seconds = capacity (mAh) x 11 / max current on the ground

FunJet race using a 2.400mAh battery discharging at 42A Max: 2400 x 4.2 / 42 = 240 seconds, or 4 minutes.
F3A aerobatics using a 4100mAh battery discharging at 52A Max: 4100 x 7 / 52 = 552 seconds, or 9 minutes.
Piper Cub flight using a 3000mAh pack at 34A Max: 3000 x 11 / 34 = 970 seconds, or 16 minutes.

Fly longer: add a cell!
The last magical number gives you an estimate of how much energy a battery stores:

E = capacity (in Ah) x voltage

For instance, did you know you can fly longer with a 3S 1000mAh lipo than with a 2S 1300mAh...? Indeed, to get the same flying style, the 2S at 7.4volts needs to discharge at 13.5A for 100 watts of power. The 3S needs giving only 9A for the same power. Using the time formula, we get a 'No Stress' flying time of 20 minutes for the 3S vs 18 minutes for the 2S. As a bonus, the lower discharge 'C' rate on the 3S battery means it will last longer.
The magic number tells the same story:

Energy in the 2S: 1.3 x 7.4 = 9.62
Energy in the 3S: 1 x 11.1 = 11.1

Some will say that a lower voltage usually means a larger prop and better efficiency. True, but the higher 'C' discharge and current on the motor cause losses that cancel the expected benefits.

Demonstration on my P-40 Svenson (170cm span, 4kg AUW, Motor HXT50-55)
The motor uses 51A Max current on a 6S lipo. The voltage magic number predicts 20 volts so we can estimate the power: 20v x 51A = 1020watts or 1.36HP. This plane has more than 250 watts per kilogram, it is powerful and climbs vertically, just like the magic formula says: 4gr x 1020 = 4080gr thrust. But beware of the excess heat buildup because the motor weights only 320gr! In theory, it should not be used above 320 x 3 = 960watts. However, on this plane the 26 cm air intake and 34 cm air exit provide optimal cooling.
2.5mm power cables are used for efficient current transfer. The motor has a KV of 500, it runs at 20 x 500 x 3/4 = 7500 rpm. The prop is a 15x8", which gives a max speed of 8 x 7500 / 800 = 75kph, which is ideal for this warbird. I use a 4400mAh battery, So I can fly for 4.400mAh x 11 / 51A = 949 seconds or about 16 minutes of cruising 'No Stress' performance.
the battery is sold for '20/30C' and could deliver a maximum of 20 x 4400 / 1250 = 70.4A peak and 20 x 4400 / 1500 = 58A during one minute. I must avoid flying continuously at full throttle because I would discharge the pack above its safety limit: 20 x 4400 / 2000 = 44A...
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Old 11-19-2007, 09:12 PM
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Very informative. Nicely done.

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Old 11-19-2007, 09:34 PM
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Wow. Great write-up!
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Old 11-19-2007, 11:24 PM
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Thanks Orion! very good info and tutorial.

Just like your planes... very detailed. Thanks

Last edited by firemanbill; 11-20-2007 at 02:46 AM. Reason: typo
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Old 11-20-2007, 02:34 AM
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You need to make this a sticky.

Mainly because I'm going to have to read it over a few times. I still find all this confusing.
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Old 11-20-2007, 02:45 AM
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Originally Posted by FlyWheel View Post
You need to make this a sticky.
I agree! Very nice write-up! A sticky it is!
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Old 11-20-2007, 03:11 PM
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What a Masterpiece Orionrider! First thing I`ll do after posting appreciation will be to copy your much valuable article in a permanent file.
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Old 11-21-2007, 11:44 AM
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Thanks to all for the kind words
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Old 11-28-2007, 03:39 PM
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Thumbs up I am saving that one as a reference!

I applaud your effort on the write up. I plan to print it and keep as a reference in my shop. I am always introducing new electric flyers to the sport and this should be required reading.
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Old 11-29-2007, 08:12 PM
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huh! oh !You forgot one thing orion" you're not an experienced electric R. C. flyer till you've burned up a lipo battery once or twice.
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Old 12-25-2007, 05:53 AM
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Excellent Job Orionrider,
Thanks for this kind of info... nicely done.
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Old 12-25-2007, 03:15 PM
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A lot of info here for this old man to take in at one time. Just reminds me of the days when those before me did all the experimenting to come up with the right combo's for the IC setups. I read about guys using such and such engine with so and so battery with someones esc-bec. Then I go to Tower to try and find the combo and the plane to put it in. Then I went to the local hobby shop and find I can get a complete electric set up that all I have to do is assemble the plane, charge the batteries and go fly. It is fun to watch the guys fly the electics, but, to an old hard head like me I fill the fuel tank, flip the prop and go fly. Then I land, fill the tank, flip the prop and go fly again. Some times I just sit and visit so someone can fly on a shared frequency. Maybe I will get an electric set up like I want. MERRY CHRISTMAS to all. DOC Holliday
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Old 01-07-2008, 11:47 AM
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Hey Doc, I still have one IC engine, an old .20ci 4-stroke from OS. The smallest 4-stroke they ever made. I just can't get rid of it

As for electrics, yes it takes much trial and error, just like it takes some time to learn how to adjust the needle(s) on a carburetor...
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Old 01-09-2008, 06:12 PM
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Unhappy I must be an idiot

I keep reading it and reading it but I'm no less confused now than I was when you posted it.

Maybe I should stick to RTF's

Last edited by FlyWheel; 01-09-2008 at 10:54 PM.
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Old 02-19-2008, 10:54 AM
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Just saved a copy to a permanent file on my PC. This is too valuable to leave. Thank you Orion
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Old 02-24-2008, 12:42 PM
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Thumbs up perfect !


thanks a lot for this info, it's great. Just what i was looking for. I've searched at several websites and forum's for this

Since i'm pretty new to modelflying, i was deeply interested in how to choose the right setup. Not just to follow what anyone is telling me ... but by thinking, counting & measuring the values. Boy, am i happy with this

Thanks again & happy flying from the Netherlands
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Old 02-27-2008, 08:00 PM
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Nice writup in good understandable English.

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Old 02-27-2008, 09:23 PM
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Last edited by RCEFlyer; 10-10-2009 at 05:44 PM.
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Old 04-01-2008, 07:46 PM
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Great article, Orion!
Wish I'd had this three years ago!
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Old 04-16-2008, 02:39 PM
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Hi you all,

im still calculating using this thread, but i do have a question about this formula.

Round and round
You always wanted to know what the famous 'KV' stands for? This indicates the number of revolutions per volt provided by an electrical motor. It gives us the 'nominal' rpm of a motor on a plane.

rpm = KV x volts x 3/4
Is this the way you calculate with efficiency ?
For example: in the specs of motors you often find Eff. = 74% or so.
Dou you use the 3/4 for this reason ?

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Old 05-09-2008, 11:51 AM
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Hi Menno,

The '3/4' factor is needed because the motor can't reach it's predicted max revolutions when there is a prop attached to it. Without prop, the '3/4' factor is not needed, but then the plane can't fly

Efficiency is something else. It measures how much internal loss there is in the motor. It depends on wire gauge, friction, design and many other things.
Electric motors have different efficiency figures depending on the load you put on them. Let's say you buy a motor that is good to run up to 30A. The advertised efficiency is 80%, but to get 80% efficiency you have to run the motor at 12A, which is not very practical. What really matters is the efficiency of the motor at 30A, and that will be more like 68%, or even less.

You could of course buy a larger motor and run it at low power to get the best possible efficiency. But it would be heavier, which in turn would degrade the overal performance of the plane. So in my opinion, advertised efficiency is not really important.
By the way, you can safely assume the efficiency is the same for all brands, give or take a few %.
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Old 08-21-2008, 06:46 AM
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Fantastic! Great resource for newbies and not so newbies.

Really minor correction, affects nothing of consequence, but I'm compulsive about accuracy... Gold is actually a worse conductor than copper. From best to not as good, to goes: Silver, Copper, Gold, Aluminum. Gold is used on edge connectors in computers not because it is a better conductor, but because it does not corrode.
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Old 08-21-2008, 09:50 AM
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Hi Orionrider,

thx for your answer, now (i hope) i'm less a newbie when i'm choosing the right setup for my planes

By the way, i've got another question. When calculating the power of a system (in theory), i assume that this is not the real power the system is gonna deliver ? But hey, do we still use this as a target for choosing the motor for the plane ? Please help me out choosing a powersystem for my new plane ... i've done some work already

For example:
i'm building a Cessna L19 Birddog (yeah, some pics are eclosed ) which wil probably be about 2,5 kg AUW. Winspan is about 150 cm (60")

So: buy your watts per kilo:
While this is a high wing plane with a reasonable wingload, i wil need about 150 to 200 Watts, right (by the way: power is nothng without control )

To calculate the power of a system i need to use the formula:
P (in Watts) = U (in Volt) x I (in Amp)

I will use a Lipo 3S or 4S for this plane, and probably a Turnigy engine like the TR42-60C, if suitable ...

On 3S P = U x I = 11,1V x 38A = 421,8 Watt ? (in flight: 10V x 38A = 380Watt)
On 4S P = U x I = 14,8V x 38A = 562,4 Watt ? (in flight: 13V x 38A = 494W)

Link to the motor is here.

Using your magic numbers i calculated that a prop 12 x 7 will be more than good ? Rpm = Kv x V = 500 x 13 = 6500 Rpm & Airspeed = (pitch x rpm)/800 = (7 x 6500)/800 = 56,88 kmh. (on 3S: 500x10=5000 & (7x5000)/800=43,75 kmh)

I couldn't find anything about choosing a ESC but i quess you only have to be sure that its capable of handling the max Amp's the system will need ? So in this case a 60A ESC will do ? I'm thinking of this Turnigy ESC60A.

Now i need to make a decision of the Lipo;
I need a battery which can suplly 60A at minimum so a 3S or 4S / about 3500 mAh / 20C will do right ? I'm thinking of a Zippy Lipoly. Link for 3S or 4S.

About the flying time, i'm confused here. Here's a quote from your conclusion: "I use a 4400mAh battery, So I can fly for 4.400mAh x 11 / 51A = 949 seconds or about 16 minutes of cruising 'No Stress' performance" But what does de #11 mean ? I will try to understand the complete article, so help me out please

Let's say this 11 is ok, in my case:
(3500 mAh x 11)/38A=1013,15 sec = 16,9 minutes flying time Right ?
Or should i calculate with the max load ?

In the last part i'm running confused again quote: "the battery is sold for '20/30C' and could deliver a maximum of 20 x 4400 / 1250 = 70.4A peak and 20 x 4400 / 1500 = 58A during one minute. I must avoid flying continuously at full throttle because I would discharge the pack above its safety limit: 20 x 4400 / 2000 = 44A..." But hey, where do the 1250/1500 numbers came from ???

Anyway, my case:
(20 x 3500)/1250 (?)=56A or (20 x 3500)/1500 (?)=46,7A
This plane will not fly full throttle continouisly, so far no problems i guess ?

Some other questions:
  1. I used the max eff A = 38A for calculating. (Max load = 52A.) Is this ok ?
  2. I guess the 4S Lipo will be the better choice with this engine ?
  3. Will the 500 Kv be ok for my kind of airplane, i'm not really understanding the Kv story so far
Please correct me if i'm wrong, i must say electric flying is cool but confusing sometimes ...

Now i'm aware of keeping you busy with my questions, but hey ... you've started such a nice thread :mrgreen:

Thx in advance .


This is how far i am building the Birdog:

This is the colorscheme i'm aiming for ...

So thanks for helping me out, getting my Birddog RTF

Last Question, is it ok if i use your article for a dutch forum ( ? I will indicate you as the author / writer of it ofcourse. Just for my fellow modellers ...


Last edited by RCEFlyer; 09-09-2008 at 05:09 PM.
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Old 09-09-2008, 03:32 PM
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Dag Menno,
Geen probleem, doe maar

Now for your many technical questions...

FYI: my 170cm Pilatus is a bit heavier compared to your plane. It flies very well with 4S 3200mah lipos, a 11x7" 3-blade prop, 60A ESC and 600KV motor.

Your choice of 500KV motor could be a problem. With a 12x7" prop, you will not get 38A. My Pilatus does 27A at full throttle, so expect something like 23A on yours. You can either increase the prop size (13x8") to get more power or buy a (lighter) motor with a 'faster' KV (600 to 700), for instance:

But even so your plane would fly. The Bird Dog is a very light machine that requires little power.

You will need a separate UBEC or rx battery to power the receiver because the BEC included in the ESC would get too hot with 4S lipos:

Remember: when using a separate power source (UBEC or rx battery) you need to cut and isolate the red conductor on the 3-wire ribbon going from the ESC to the receiver. Otherwise, power from your UBEC or rx battery will discharge in the ESC, which will likely destroy it.

Many happy landings!
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Old 10-20-2008, 11:35 AM
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This is an extremely well written piece. For that alone you should be proud. There are many useful articles on Wattflyer but many are poorly written. Yours is excellent.

While much of your content is familiar, there are elements that I have not seen before. You give no reference links so I presume some of this has been developed from personal experience over time.

For example your 3/4 ratio for the Kv RPM. I don't recall seeing that before. Is that an industry standard or just your practical observation?

Your heat dissipation ratios of motor weight, in grams, to max watts is another example. I have never seen this before. An interesting ratio. How is it developed? Does it hold true for very small as well as very large motors?

Your thrust ratio of grams of thrust per watt is also new to me. It would seem this is highly dependent on prop and battery combinations. Are you giving general guidelines or is there some engineering ratio at work here? Again, does it hold true for very small as well as very large motors?

I do not presume to challenge you on these points. I am just interested as to how they were developed. Are they practical observations or engineering formulas, like Watts = Volts X Amps?

Again, a very well written piece.
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