Horsepower and Golf Carts

As a person interested in technical stuff, the definition and usage of the term horsepower, has always intrigued me. The following is the best I can do to summarize what I have observed, as I have studied the subject and sort of how it relates to golf carts.

The definition of horsepower came from a gentleman named James Watt, who, in order to pedal (sell) steam engines, around the turn of the century, needed a way to compare their ability to do work with a horse. The engines would soon take over much of the work being done by horses, so it only made sense, to use them as the standard.

Mr. Watt studied what horses could do and came up with some numbers that have been challenged by many, but at least he provided a way to discuss and compare things and put numbers on them.

He concluded that an average horse could pull with a force of around 180 pounds, and while doing it, could walk about 181 feet per minute. Then he multiplied the 180 pounds (lbs.) by the 181 feet (ft.) and said it equaled about 33,000 ft.-lbs. of work that was being done per minute. Lots of people argue that a horse couldn’t sustain that level of energy for very long, but, what the heck. The number has stuck with us for many years, so, like it or not, 33,000 ft.-lbs. of work done in a minute’s time is called one horsepower.  

Interestingly enough, the way that one horsepower is defined would accommodate a scenario where a 33,000 lb. weight was moved only one foot in one minute. Now we all know that there isn’t a horse on the planet that could move a 33,000 lb. weight one foot, no matter how long you gave it, but the numbers still match the formula. In trying to lift the 33,000 lb. weight, the horse would exert as much force as he could muster up, but because the weight didn’t move, by definition of the word work, no work was done. Likewise, moving a one lb. wight 33,000 ft. in one minute would also match the formula, but to do that, the weight would have to travel at 375 miles per hour. (33,000 ft. divided by 5280 ft. in a mile, multiplied by 60 minutes per hour). I don’t know of a horse on the planet that can run that fast, but the numbers still fit the formula. In trying to move the one lb. weight 33,000 ft. in one minute, the horse will do work, but it won’t come up to the definition of one horsepower because the weight didn’t go far enough. However, the formula is usually used under more reasonable circumstances (with values more in the middle of the range) and becomes more useful when applied to things like automobiles, golf carts, motorcycles, and other machines, as they are used in their normal fashion.

Since motors (internal combustion, electric, etc.) deliver their power by spinning a shaft, we now need  to relate horsepower to things that spin in circles. When we measure the power that a motor can exert (and therefore the work it can do), we use a term called torque. Torque is the twisting force that a spinning shaft exerts, and is expressed in ft.-lbs. The torque of a motor can actually be measured with a device called a dynamometer, and then the horsepower can be calculated from the torque measurement.

In order to demonstrate how it works, we will use an imaginary motor to spin a one lb. weight around in a circle one foot away from the center of the circle. Now this weight is not skidding along a surface, because that would cause friction. Our imaginary motor is just supplying enough torque to move one lb. of weight around our circle that has a radius of one ft. (two ft. diameter). When the motor spins one revolution, the one lb. weight will have moved around the circumference of the circle. The circumference is defined as π (pi which is 3.1416) multiplied by twice the radius (C = π 2 R). So, in our case, C = 3.14 x 2 x 1 = 6.2832. So, 6.2832 ft.-lbs. of work was done. If we take the 33,000 ft.-lbs. of work that we need to do in one minute and divide it by the 6.2832 ft.-lbs. that we did (33,000 / 6.2832) we come up with 5252.10. We’ll call that 5252. That is how many times the motor would have to spin the shaft in one minute in order to fulfil the definition of a horsepower. It would have to spin at 5252 RPM (revolutions per minute).

So, in review, if a one lb. weight is moved 6.2832 ft., 5252 times per minute, 33,000 ft.-lbs. of work will be done, and that is equal to one horsepower.

Now, of course, it wouldn’t matter if the weight was two lbs. and was only spun around 2626 times per minute We would still have done the same amount of work.

So, with that in mind, the following formula would describe the situation:

                Horsepower (HP) = Torque x RPM/5252

In our case:

                1 HP = 1 ft.-lb. x 5252 RPM /5252

So, if we looked at a motor that delivers 500 ft.-lbs. of torque at 3600 RPM:

                HP = 500 x 3600/ 5252 = 342.72 HP

Had the 500 ft.-lbs. been delivered at 5252 RPM:

                HP = 500 x 5252/5252 = 500 HP

The torque and the horsepower only come together at 5252 RPM. At any other RPM, there will be a difference between the torque and the horsepower.

Now to get to how this stuff relates to golf carts. Let’s start with gas carts.

Most golf carts that have gasoline engines have a horsepower rating that is published by the manufacturer. So, you can find that rating by going to the owner’s manual (usually), the internet by researching its model number or serial number or by contacting the manufacturer. It’s the same horsepower rating system that we have been discussing so it will make sense. American made gas carts are required to conform to SAE J 1940 standard when stating their power. The standard calls for the horsepower to be stated for performance at 3600 RPM and the torque rating has to be stated at 2600 RPM. So just for kicks, I went to the Owner’s Manuals for a Club Car, an EZ-GO, and a Yamaha to take a look in the specifications and see what they said about power.  All three were 2015-2016 era carts.

                The Club Car stated the power as 14 Horsepower at 3600 and referred to the J1940 standard.

                The EZ-GO stated the power as 13 Horsepower at 3600 and also referred to the J1940 standard.

The Yamaha stated the power as 11.4 Horsepower at 3500 RPM with no mention of the J1940 standard (I assume it has to do with its foreign manufacture).

Without any statement about torque or any kind of a chart to relate torque vs RPM, there really aren’t a lot of conclusions that you can conjure up. We know that horsepower is the same as torque at 5252 RPM, but with a gas engine, who knows what the torque is at 3600 RPM? It really doesn’t matter, because some kind of an RPM limiting system is going to kick in at a predetermined (but probably unpublished) point anyway. Another thing to remember when it comes to horsepower is that the J 1940 Standard states that the horsepower is to be stated in “Gross” output. That means that the engine is tested without an air-cleaner system, without a muffler, without a starter/generator, etc. All of the things that either add restriction to airflow or add resistance to power output of the engine are removed. Also in the testing, the ignition timing has to be set at an optimal setting (not advanced or retarded from how the engine will be normally used), and a formula is used to mathematically adjust the output rating to compensate for atmospheric conditions. So, the Gross output number is intended to reflect the engine’s performance under ideal conditions. I did some comparisons of Gross and actual outputs of several engines that I could find documentation on, and the actual horsepower turned out to be between 9% and 15% less than the published Gross amounts. In order to establish a more realistic standard to evaluate the output, there have been newer standards that reflect Net output. This standard takes into account the presence of a exhaust system, some accessories, etc., and produce a more user friendly number. As I understand it, the Net horsepower standard is not used on smaller engines like those in golf carts. Only the J 1940 is applied.

Now let’s take a look at electric golf carts with DC motors. The output power of a DC motor is generally indicated as a horsepower rating, but there are many strings that can be attached.

The power that a DC motor will put out is affected by its RPM, voltage applied to it, and of course the load that it is trying to operate at. There is a long list of terms that are used to describe the performance and design of DC motors, but I will limit this discussion to the most important ones, and the ones that you might find published by the manufacturer and on its label.

There are two kinds of DC motors that are commonly used in golf carts: Series and Shunt.

Let’s start with Series motors. In a Series DC motor, the armature and the field coils are wired in series with each other (as the name indicates), so all of the current that flows through the system (battery pack, forward and reverse switching, and motor speed control), flows through both. Therefore, if the voltage to the motor is increased, thereby increasing the current, both of their magnetic fields are increased proportionally at the same time. In order to reverse the direction of travel of the armature (and therefore the direction of the cart) the relationship of phase (direction of current flow) through the armature with respect to the field is reversed. Because the amount of current involved is significant, this requires a pretty rugged switching device that can withstand the load, and this can become problematic with wear and tear over the years. Even a small amount of contact resistance can lead to heat problems.

Let’s look at how a typical Series DC motor works.

As we first apply a voltage to the motor, the current that flows is defined totally by the resistive properties of the field and armature windings. Since these are constructed with coils of large wire of very low resistance, the resistance to current flow is very low and the current tries to go VERY HIGH instantaneously. Thanks to a phenomena called CEMF (which is explained in just a minute), this situation doesn’t last for very long. This large amount of current is referred to as the motor’s Stall current, and could not be tolerated by the windings, the source, any kind of speed control devices, the motors wiring, etc. for very long. But, as soon as the armature turns, something happens called the generator effect. A voltage is induced in the armature that is proportional to the speed that the armature spins, and is opposite in polarity as the source voltage. The voltage is referred to as a Counter Electromotive Force (CEMF). This means that the net voltage acting in the series circuit is equal to the supply voltage minus the CEMF. So, once the armature starts to spin and the CEMF begins, the current through the armature (which is producing the torque) begins to lower and therefore, so does the amount of torque being produced. So, our output torque goes from the Stall torque to a reduced amount of torque produced by the smaller amount of current effective in the armature. If left suppled with the same source voltage and not loaded, the armature will continue to increase in RPM up to a point that is limited by the design of the motor. When it reaches this limit, the RPM is called the motor’s No Load speed. As it climbs to this speed, the CEMF is constantly increasing, the difference between the supply voltage and the CEMF is decreasing, and the current through the armature is decreasing proportional to the RPM. At the No Load speed, the supply voltage and the CEMF are practically the same. The only reason they aren’t is due to inefficiencies in the motor caused by losses due to resistance of the windings, friction of bearings etc. Only enough difference between the supply voltage and the CEMF exists to produce enough current to produce enough torque to keep the armature spinning. At this point, the torque has gone all of the way from a very high number at Stall current and torque to a very small number, just enough to keep the shaft spinning at the No Load speed. Now, let’s suppose that we reached over and grabbed the shaft with our fingers and drug its speed down a bit. As the shaft begins to slow, the CEMF will fall a bit, thereby increasing the difference between the source voltage and the CEMF voltage and therefore increasing the current through the armature and therefore increasing the torque on the shaft. The motor, more or less, tries to maintain the speed of the armature because of the drop in the CEMF.

As current flows through the windings of the armature and the field, it, of course, meets a certain amount of resistance which causes heat. The motor’s ability to dissipate heat becomes a very important factor in the process and most motors have methods of shutting themselves down if a certain heat threshold is met (thermal protection). When a designer needs a certain amount of torque from a DC motor, he selects a motor that can comfortably sustain a level of current proportional to the amount of torque needed at a reasonable RPM and level of heat production.

 In the application of most DC motors, there is a nominal torque that is supplied to a nominal load. So once the motor gets to its nominal speed and therefore produces its nominal torque, things are pretty straight forward. The horsepower that is at work can be calculated with our conventional formula: HP = Torque x RPM / 5252 (as explained above). So, if we had a motor that was required to supply 2 ft.-lbs. of work at 2626 RPM, the HP would = 1 (2 x 2626 / 5252 = 1). 

Now let’s take a look at DC Shunt motors. The difference is that the field windings in a shunt motor are not wired in series with the armature, but are supplied by a separate supply of their own from the motor speed controller. The motor speed controllers used for Shunt motors are generally microprocessor (computerized) controlled and offer a bunch more versatility than Series motor speed controllers. Because the field voltage and current can be separately manipulated by the controller, a thing called “field mapping” can be used to offer many different variations of current and voltage to the field to fit a variety of different conditions that might arise in operating the cart. The field supply can even be shut down or limited by the controller if the controller detects something going wrong that might damage things. Things like overheating, low supply voltage, stalled armature, component failure, etc. The controller can even reverse the polarity of the energy used by the field to provide a way to reverse the direction of the rotation of the armature without having to use the conventional heavy duty forward/reverse type switch used in Series motor carts. With Shunt motor controllers, the reverse or forward selection is usually made by the flip of a low voltage, low current toggle switch mounted on the dash board or “fire wall” of the cart. The amount of field current used in the Shunt motor can be drastically reduced, as it does not have to be the same as the armature current. Most of the Shunt type motor speed controllers are programmable by either a special hand-held communications module of sorts, or even by the USB port or RS-232(serial) port of a computer. Among the many parameters that can be programmed are: Throttle Acceleration / deceleration rate, Armature current limit, Brake current limit, Under / Over voltage shutdown, Half-speed reverse, High-pedal disable, and even Plug braking.     

With either a Series or a Shunt motor, the thing that is different about golf carts, is that there really isn’t a nominal load or nominal RPM. We vary the voltage to the motor to vary the speed of the cart. The motor doesn’t just come up to a set RPM (and therefore a set torque output) and stay there. Every time the accelerator is moved, the RPM, torque and horsepower are all affected.

So, what does the horsepower rating of the DC motor really tell us?

In order to answer that question, I went to the owner’s manuals of three more golf carts, once again a Club Car, an EZ-GO and a Yamaha to see how they stated their output power.

The Club Car only referred to its output as 3.1 HP. No reference to RPM, torque, or anything else. It did state that the system operated at 48 volts.

The EZ-GO stated 2.5 HP at a continuous speed (who knows what speed?) and 18.1 HP at 1900 RPM.

The Yamaha did not make a statement about HP at all, 12 MPH (factory) and 15 MPH (maximum). I did go to the internet and looked up replacement motors for the Yamaha and one of the manufacturers stated 4.3 HP at 3500 RPM and another stated 4 HP at 4400 RPM.

As you can see, there isn’t a strong agreement among manufacturers as to how this matter of output power should be handled. It seems to be just kind of a reference, leading us to believe that the bigger the number, the better.

Even though DC electric motors for golf carts are often rated in terms of horsepower, it’s not quite like discussing power output of internal combustion engines which have many things about them that affect when the peak torque (and therefore horsepower) over a range of different RPMs. Things like carburetors, valve overlap, valve timing (camshaft design), fuel octane, compression ratios, and so forth and so on, are designed specifically to develop torque with a unique relationship to the RPM. A DC motor doesn’t work that way. The torque that is produced by the motor is proportional to the voltage applied, the RPM that the motor was designed to run at, the amount of current applied, and of course the load that is applied.

Another thing that complicates things, is that some of the ratings published for DC motors rate them at Peak horsepower. Remember the instantaneous rush of current through the circuit when a source voltage is first applied to a DC motor (Stall current)? Well, that is the current that is associated with Peak horsepower. When the current is at its highest point, of course, the torque and therefore the horsepower is at a very high level, but only instantaneously. The motor couldn’t sustain that level, but that is the Peak horsepower that they are talking about. That’s hardly any usable information with regard to the overall performance of the golf cart.

So, if we take, for instance, one of the golf cart DC motor ratings that we looked at before, what does it do for us? In my opinion, not much. If it just gives a horsepower of 3.1, that doesn’t tell us much. We don’t know what the RPM is for that horsepower, so the horsepower (as in the case of gas golf cart engines) just becomes a reference for comparison to other golf carts’ ratings. We could convert the horsepower to watts, that’s easy enough. We know that one horsepower is equal to 746 watts, so 3.1 x 746 = 2312.6 watts (2.3126 kilowatts). If we assumed that the wattage was being supplied by a 48 volt source (common to golf carts) then we could calculate a current draw of 48.17 amps of current. But they don’t really tell us that the horsepower is stated for a particular voltage or RPM, so who knows.

As I mentioned at the beginning of the article, the definition and usage of the term horsepower has always intrigued me. It does seem, however, that the more I know about motors in golf carts, the less I really know about motors in golf carts!

Ron Staley has published the following books, and you can get more information about them by just clicking on each title below:

Electric Golf Cart Repair 101 (and a half)

                Techniques, Tips, Tools and Tales

Gas Golf Cart Repair 101 (and a half)

                Techniques, Tips, Tools and Tales

Suck, Squish, Boom and Blow

                4-Stroke Golf Cart Engines Explored

Those Darned Slot Machines

                What Makes Them Tick

                By an old Slot Machine Mechanic