Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I need formulas explaining Voltage and Amperage

  1. May 23, 2014 #1
    I had been looking at my Grandpa's Trike and here are some of its stats:
    1 HP 24V 42.4A 3200rpm (battery 2 12V 700-800A connected in series)
    my concluded watts per horsepower about 1017.6 w/HP

    Now a different motor
    Tesla's Model S's motor
    416HP 2 motors 85kWh battery
    concluded watts per horsepower about 214w/HP
    *I don't know its Voltage and Amps exactly*

    According to Physics: Electric conversion to mechanical is 746 w/HP. So why does my Grandpa's trike have more wattage per horsepower than a Tesla S and the Physics value? And the Model S has less than both values?? Thats what I don't get.

    Does amps express "supply" and Voltage expresses "pressure" or "power"?
    Or is there anything that voltage and amperage do to electric motors? If there is, can anyone send me formulas expressing it?

  2. jcsd
  3. May 23, 2014 #2
    you can't have a watt per horsepower because they are both measurements of the same thing.

    the basic formula is P(watts)=V(volts)*I(amps)

    One thing that might help you is to look at what the units are 'made of'. For example, a volt is a watt per amp, and it is also a Joule per unit charge. Hence a volt determines the amount of energy per electron, so it is similar to a pushing force. An amp is a unit of charge per second, so it is exactly like a flow.
  4. May 23, 2014 #3

    jim hardy

    User Avatar
    Science Advisor
    Gold Member

    1. Grandpa's trike motor is not 100% efficient. Some of the watts that go in as electricity are spent in heating the armature windings(and field too if it's not permanent magnet), in voltage drop across the brushes, in forcing cooling air through it, likely some in bearing and gear friction , etc. If it has an electronic controller there's yet more losses.
    If you have to put in 1017 watts to get a horsepower out, what is the efficiency ?

    2. For the Tesla you've confused power and energy, a common enough mistake.
    back to your basics - what's the difference between power and energy?
    hp is power, KW is power;
    KWh is energy

    How long can a 85KWh battery deliver 416 hp before all its stored 85 KWh of energy are spent?

    hint - a lot less than an hour.
    If they told you exactly how long theirs could do it you might be able to back-door a rough number for efficiency, but they didn't.

    I'm an old guy and would have worked this in English units, 1hp = 550 ft-lbs/sec.
    On my slide rule.
    You'll probably prefer SI.


    old jim
  5. May 25, 2014 #4


    User Avatar
    Gold Member

    One horsepower is equiv. to 746 horsepower. But, no "horsepower maker" is 100% efficient. So, it might take 1000watts in to get 1HP out. The Trike and Tesla will have different efficiency.

    Jim's points about the difference between and amp and an amp-hour are also very pertinent.
  6. May 25, 2014 #5
    I don't understand the concept, so if i apply a 20 amp motor with a 800amp battery, will it blow up or it will make it like a supply? (What I'm thinking is amps are per hour and it draws in 20, it could take 40 hrs to completely drain?)
  7. May 25, 2014 #6
    Plus by any chance do any of you guys know an inductor's energy decay formula? Like say from full applied supply to zero in how many seconds? And i need a formula to show the Henry unit so i can 'predict' how much i can have at a certain time?
  8. May 25, 2014 #7


    User Avatar
    Gold Member

    What exactly are you trying to calculate. You are all over the place, and don't have a basic understanding of volts, amps, power, and energy.

    I hate to do this "tutor" thing, but tell me the difference between amps and amp-hours.

    Also, you need to understand basic motor theory relating to power, torque, and efficiency. Trust me, you need to know nothing about inductance at this point.

    http://www.micromo.com/motor-calculations.aspx is the motor part of what you are asking. It's for small motors, but the basic concepts apply.

    Read about dc motors and try to understand the efficiency curves. How rpm, torqure, current, efficiency and power all relate in a motor. For example, a stalled motor develops the most torque, draws the most current, but delivers no power.
  9. May 26, 2014 #8

    jim hardy

    User Avatar
    Science Advisor
    Gold Member


    it would help us to understand your background a little .

    How much physics have you studied? Have you had high school physics, or are you a college graduate, or are you a young person tying to self educate?

    We often get questions from people who are looking to be spoon-fed what they should already know. That is plain laziness and we don't encourage that.

    We sometimes get questions from well meaning young people who are curious enough to explore things beyond their present level of education. That's [STRIKE]laudable[/STRIKE] to be praised.. We try to point them to material appropriate for their level.

    Check out this guy's down to earth explanations of the very basics.

    I think he'll help you sort oout the basic concepts and units.

    And let us know a little about your background..

    old jim
    Last edited: May 26, 2014
  10. May 26, 2014 #9
    I have highly functional autism, and after my grandfather moved nearby us for 6-7 years, I had begun learning motors, after that i decided to become a green activist... My ultimate goal when i was young i wanted to have "More distance with little to no fuel"... I am self teaching myself physics because my school wont let me get ahead of my peers, or jump classes (even though i fly through them anyways) I started my first idea with a 4wd pedal car, then grandpa introduced me to gasoline motors. After that i flourished my knowledge, cause i was hungry for a long period of being a "vegetable"

    So far now, i run out of brains to pick, because i am "higher leveled thinking" than my other mentors, ones include CAD/CAM/CNC teacher, automotive teacher, electrical maintenance teacher, grandpa, a few physics people. And right now, and please don't say this is an impossible task. But i am drafting an idea for an electric power multiplier, and changing the way AC motors run with the same system. I have most of the components ready. I just need equipment and advice before building said machine.

    I've pretty much know most of the concepts, and developed strategies to the "banned" objects, plus im working on something that is seemed to be impossible, but for every problem there is a solution. Either bad or good. Because I'm making the Power Multiplier Unit, it can crush me if someone made this already or stole it from me and claim it as their own. Plus i need other people(s) opinion other than thinking i have it all in the bag and get disappointed.
    Last edited: May 26, 2014
  11. May 26, 2014 #10
    Any formulas for how much time an inductor takes from full value to zilch on seconds?
  12. May 26, 2014 #11
    If you want to teach yourself, you are going about it the wrong way. Grab a textbook, read it, and understand the concepts behind the formulas. Then you'll understand how to apply the formulas. If you have questions, then you come and ask. Then work through the problems so you know you understand both the concepts and the formulas and the math. We could give you all the formulas in the world, but that wouldn't stop you from misapplying them. As it is, it sounds like you are trying to break the law of conservation of energy. Well... good luck with that.

    But since you asked, the basic equation for an inductor is v = L*(di/dt), and a good page for exponential decay is here.
    Last edited: May 26, 2014
  13. May 26, 2014 #12

    jim hardy

    User Avatar
    Science Advisor
    Gold Member

    Well, okay.

    Have you read Bill Beatty's page linked above?
    If so you understand the distinction between a watt and a watt second, that is to say between power and energy.

    And the distinctions between charge, amps, volts and watts.

    Now to your original question:
    A DC motor has an internal magnetic field , probably in Grandpa's trike it's from a permanent magnet.
    In bigger motors it's usually from an electromagnet.

    That field has magnetic flux whose value usually is represented by Greek letter phi, [itex]\Phi[/itex] .

    Applying DC voltage V to an unloaded DC motor will cause it to rotate at approximate speed RPM = V/(K X [itex]\Phi[/itex] ) .
    We usually work the other way, spin the motor at precise speed and measure its open circuit voltage

    V = K X [itex]\Phi[/itex] X RPM .
    That way there's no error due to friction and windage load.
    And there's no voltage drop due to armature current, so it's the motor's counter emf at that speed that we have measured.
    The value of K X [itex]\Phi[/itex] is a valuable piece of information about that motor.

    Having established the value of ( K X [itex]\Phi[/itex]) for that particular motor, we take note of it. Maybe write it on the side.

    Now - if we connect a power source to the motor and let current flow,
    it will make torque( in foot-pounds) = (same K X [itex]\Phi[/itex]) X 7.04 X armature current(amps).
    That 7.04 would be some other number for newton-meters, i studied motors in English units.

    So here's what volts and amps do to a motor:
    V = K [itex]\Phi[/itex] RPM , not counting armature resistance
    More volts tends to speed it up
    torque = 7.04 K [itex]\Phi[/itex] Iarmature
    loading the motor down slows it, reducing counter-emf, allowing more current to flow from the source through the armature, making more torque to carry the load at the new RPM.

    So in summary :

    Counter-emf voltage = K X [itex]\Phi[/itex] X RPM
    Torque foot-pounds = 7.04 K X [itex]\Phi[/itex] X Armature amps

    If you measure armature resistance you can predict the motor's behavior as follows:
    Armature Current = (Applied Volts - Counter EMF)/(Armature Resistance) .
    So using the two equations above, speed and torque are easily predicted for any combination of torque and applied voltage..

    You can find more sophisticated explanations with searches on some of those terms, and on " DC Motor theory" ..

    DC motors are delightful toys. I keep a few old car generators and windshield wiper motors around for projects.

    Have fun,

    old jim
    Last edited: May 26, 2014
  14. May 26, 2014 #13


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    1 horsepower is equivalent to 746 watts. That's the SI conversion between the two units of power.

    You can also say '746 watts per horsepower' with the understanding that one is referring to a figure for unit conversions.

    Saying 1 horsepower is equiv. to 746 horsepower is non-sensical.
  15. May 27, 2014 #14


    User Avatar
    Gold Member

    And obviously a silly "typo". Any moderator should feel free to correct it for me.
  16. May 27, 2014 #15
    I had studied portions of the Capacitors, Inductors, and a bit on magnetism using a college Physics book...
    And I'm apparently lost. One says wattage and HP are the same? some say differently, I thought it may be a conversion unit because if you applied certain wattage, you obtain a certain HP as your output. But as a few had said earlier that there were efficiencies, I figured it out... Thanks for your help guys!
  17. May 27, 2014 #16
    power can be expressed in watts, or it can be expressed in terms of horsepower. Its still the same thing. You just have to scale them to make them interchangeable. not any different than feet and meters. so when you said you have 1KW/HP, its kind of like saying you have 5 feet per meter, which is obviously very strange.

    Now your 24V * 42A is your maximum input power. Your 1HP is your output power. When you divide them, you end up canceling the units and replacing them with a scaling factor (1/746 here) and the number you get is a unitless ratio of input to output. essentially efficiency, but you did it backwards. Efficiency is Pout/Pin because Pin is always greater than Pout. This is why I caution you on just being spoonfed the formulas.

    Unfortunately, things are still more complex. You are neglecting the efficiency of the battery entirely (the amount of total energy you can squeeze out reduces as current increases) for starters. You are also trying to compare your motor's efficiency against the Tesla by using its battery energy instead of its input power.
    Last edited: May 27, 2014
  18. May 27, 2014 #17
    i am fully aware fo you saying I'm being spoon-fulled and not doing it right, But i know exactly how to solve for efficiency. Its (Wmotor-Wconstant)/Wconstant. I get that already. I was saying the drawing in of wattage saying it takes 1017 watts to run one hp on the trike. Yes I'm fully aware they are equivalent. The SI unit for HP is either Joules/sec, and/or VI. The english HP is (lbs*foot)/550. I am merely using this as a conversion tool.

    This is what im trying to point out: (or at least trying to say)
    For example, 900w going into the trike, the HP equivalent will be 0.885HP because i converted watts into HP equivalent.

    All I did was plugging in 900w from 1017w/HP to solve for HP. This is a mere shortcut to solve for HP. I could have done 900*efficiency(or 746/1017 or whatever)/746, because its the exact same thing. Both formulas solve for HP, from inputting wattage. Even though 900 will have more than 1HP because of 746 watts, but thats assuming at 100% efficiency though (which is not real).
    1 HP= 746W (VI) or ((lb*foot)/550)

    I hope this is what you are saying Mrsparkle, because I think I have my words mixed up.
    Last edited: May 27, 2014
  19. May 27, 2014 #18
    The Wconstant is reffering to 746w equals one HP.
  20. May 27, 2014 #19
    I did noticed however on the whole battery situation, because i dont have ALL the information, therefore i can't really compute it right. Thats why I am lacking formulas to string up a calculation to help explain it. If I can basically string it all up together, I wouldn't be on here asking.

    Do you have any formulas regarding battery efficiency as you said? Because it can help me understand DC better.
  21. May 27, 2014 #20


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The definition of 1 HP is 550 ft-lb/sec or 33,000 ft-lbs/min. There must be a time unit somewhere, since ft-lb is the unit for work or energy, while power is the rate at which work is done.
  22. May 27, 2014 #21
    oh oops lol I forgot to write it correctly, thank you Steam!
  23. May 27, 2014 #22
    Saying watts per HP sounds very strange and it is tripping you up when you look at the Tesla. Look at it this way. Convert all HP to watts. So your motor is 746W and the Telsa's is 310KW. Now you are saying your motor gets 1017W per 746W. This sounds strange, and makes people think the wrong thing when they hear it. So flip it around, cancel the units, and do the division. You get a ratio of 0.73, meaning your motor is 73% efficient (at peak power). This is a much more clear.

    And doing it this way should make it much more obvious to see the problem when you compare it to the Tesla. If you divide 310KW by 85KWh, you'd get an answer of 3.64 per hour. That is clearly not an efficiency ratio, so you would know you couldn't compare it to your 73%.
  24. May 27, 2014 #23
    It can't be approximated down to a simple formula. There are various chemical reactions going on in there that are governed by a number of different things that vary by battery type. You'd have to look at the graphs in the battery's datasheet.
    Last edited: May 27, 2014
  25. May 27, 2014 #24
    Ineffectively, my point is wrong when you put in 746 replacing the HP on the other side of the equation into my 1017.6.... you forgot to mention in efficiency in this.
    efficiency*1017.6=746 aka balanced. (efficiency is 46.8%)

    Now you had put in 746 watts on the opposite side, which wasn't necessarily true, unless efficiency is put in that equation to make it equal to 746 watts.
    so if you tell me I have 1000 watts you are going to say 1000 isn't equal to 746 watts theoretically making my point ineffective. I do understand when you were trying to balance it with efficiency, now get this. What is the efficiency of a motor with 15000 watts having a 25HP output? So, divide 15000/25 and you get 600 watts per Hp, divide 600 watts from one HP to 746 watts for its one hp (James Watt's constant). The motor efficiency is 80.4% since 600/746. IT TAKES 746 watts to EQUAL 1 HP. Therefore 746 watts PER HP. 746w/HP
    Last edited: May 27, 2014
  26. May 27, 2014 #25
    Even YOU said efficiency had to be considered in the equation. Unless my calculations are wrong when I gave you 15000 watts and 25HP, then prove the inefficiencies and everything. I merely use this as a tool to convert inputted wattage to outputted HP.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook