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Number of coils and rpm

  1. Mar 21, 2008 #1
    Hello guys, I am curious about the effects of increasing the number of coils on the armature of a DC electric motor. Say if I switch from a coil from 80 turns to one with 160 turns (made of the same material) would the rotational speed of my motor decrease for the same voltage?

    I had several ideas but can't make them connect.

    1. Since more wires = larger resistance and if voltage stays the same, there would be less current. However, current affects torque and not rotational speed. (since torque = NIAB) Torque and rotational speed, unless I am mistaken, are not exactly related.

    2. More coils = increased torque but like I said above, I don't see the connection between torque and rotational speed.

    3. I read something that rotational speed is proportional to voltage, and since voltage is constant, the rotational speed of the larger and smaller coil should be the same.. I interpreted this from this thing I found online..

    'Torque' is what makes 'outrunner' motors special. Torque on any motor can basically only come from combinations of:
    1. strong magnets (eg: 'N' number, size and coverage)
    2. efficient flux path (eg: rotor & stator size, materials, design & construction, air gaps)
    3. greater diameter (more 'leverage')
    4. many magnet poles
    5. many turns
    6. high current
    7. gearing.
    These motors are ideally suited to exploit all of these. However, the last two tend to have negative implications so are avoided in most outrunner designs.

    Characteristics that increase RPM are the opposite of all the above (except current probably). In addition, RPM is roughly proportional to voltage so more volts = higher RPM.

    But it doesn't really make sense that everything would spin at the same rate if given the same voltage.

    So I am kinda confused and would appreciate any input on this. Thanks.
  2. jcsd
  3. Mar 21, 2008 #2
    You are right that it doesn't make sense because it isn't valid. Each motor on its own has a unique Kv constant and a unique Kt constant that it is designed for.

    Kv, which is your back EMF constant, is usually in units like:

    V/RPM or V/(rad/sec)

    So you can multiply how fast your motor is spinning by this constant and you will get the back EMF generated. This back EMF is fighting with the voltage source you're providing, as it is the motor's natural negative feedback.

    Kt is your torque constant, and it is usually in units like:


    You can multiply the current going into your motor by this constant and you will get how much torque the motor is generating.
  4. Mar 21, 2008 #3
    So now we proved that same voltage does not mean the same rpm, would you say that the larger coil would have a smaller rpm then? I see how current is affecting torque but I just don't see how it is affecting rotational speed.
  5. Mar 21, 2008 #4
    Just in general, not DC motors specifically, but most high torque motors/engines are not designed for high speeds. High speed motors/engines usually sacrifice some torque. Unless the motor is a really good one, and probably expensive, it is going to excel for high speeds with lower torque or high torque and low speeds.

    I don't know all of the equations that can explain a DC motor, like how they design for Kv and Kt, but it is obvious that a really small coil can still go really fast as long as it has no load, but a small coil would never be used to drive a large load requiring torque. A large coil can also go fast, but it is going to have much more torque capability.

    From that I would guess that the coil size is not going to affect rotational speed directly, although I'm also sure it plays a part in the overall design of getting speed up as its part of the circuit. Keyword is guess. You are best off deriving equations and seeing how they relate, unless someone with a lot of experience can just give you the answer.
  6. Mar 21, 2008 #5
    Ok thanks for the help.

    I look a bit more online and found something.

    I took this diagram from some mit site.

    http://lancet.mit.edu/motors/colorTS1.jpg" [Broken]

    They said..

    The graph above shows a torque/speed curve of a typical D.C. motor. Note that torque is inversely proportioal to the speed of the output shaft. In other words, there is a tradeoff between how much torque a motor delivers, and how fast the output shaft spins."

    Ok, so in my cause, larger coil have more turns, and thus larger torque. Since the relationship is inverse, larger torque causes slower rotational speed. Is this reasoning correct? Thanks
    Last edited by a moderator: May 3, 2017
  7. Mar 21, 2008 #6
    Well this torque speed curve holds for any single unique motor, not necessarily the design of different motors' coils.

    For a particular motor you have more torque at lower speeds. And as speed increases torque drops as a linear relationship. Why?

    Think of the overall power of the motor, and the motor is going to have a maximum capable P.

    Also remember just from physics:

    Power = current * voltage
    and also
    Power = torque * RPM

    so if P can be a max for a particular motor, and V will determine your RPMs and I will determine Torque then there is a tradeoff for that motor at certain speeds or certain torques so that it can only be capable of the same power.


    This power relationship would also be a good way to measure efficiency by measuring the output torque and rpm and the corresponding input voltage and current

    (T*RPM)/(I*V) would give you the ratio of transferred power
    Last edited by a moderator: May 3, 2017
  8. Mar 21, 2008 #7
    Ah that makes alot sense. Thank you very very much.
  9. Mar 22, 2008 #8
    This is how it works, and it goes for outrunner, and brushless, and generally DC motors without field windings:-

    You will get double the torque for the same current.

    Your motor will run half as fast for the same applied voltage. Notice that this makes sense from a conservation-of-energy accounting.

    The wire will have about half the area and twice the length. The resistance increases by a factor of about 4.

    The motor disipates heat under load. The more load, the more heat. So for 4 times the resistance the tempurature will rise 4 times as much.

    But let's look at the heating in terms of the output torque. The torque has doubled, so the temperature will rise only 2 times as much for the same torque.

    For the heating factor I've ignored the effects of any change in motor speed which
    effects the cooling capacity of the air pushed around the windings. You should probably pad well for this, since outrunners are high performance motors and are power-rated at comparatively very high temperatures.
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