Formula to find horsepower hours

This may be off-subject, but I have a request/suggestion. In college I had some subjects that I just "got" and others I had to either memorize or at least deal with on a purely theoretical/mathematical basis. This latter approach took a lot more work, was a lot less fun and ultimately fruitless. My solution was to switch from electrical engineering to mechanical engineering, and for me that worked. BUT - I always wondered if that had to be the case. If I had a heath kit instead of an erector set as a kid would I have developed an intuitive understanding of electronics? Near the end of my first degree I did take an EE class for MEs that took the approach of using analogies, and that really worked well for me.

Anyway, I have a request to those of you who seem to have such a strong grasp of energy/power. Can you frame your answers in the form of a tangible, physical example? For instance, if the robot had a 3 foot arm swinging a 5 pound sledge, what are the forces and energy required to get the sledge up to speed? Also, ssuming one doesn't observe it too closely and get whacked, how much energy will it consume as it swings about? Better yet, how many AA batteries would it take to keep the arm running, taking into account standard efficiency ratings for motors and bearings (personally I have trouble believing air resistance is the major source of loss, but in school we always did assume frictionless bearings and perfect motors and such). This is the whole point of building a robot, in my mind: To make the theoretical tangible.

I hope this makes sense. I am not trying to be cheeky here. I honestly believe there is a difference between learning and truly understanding, and that gap must be battled in every course and every lesson until it no longer exists.

Morepower to ya! I, too, should have switched to mechanical engineering, but never did. I think every school should make an effort to explain electrical phenomena with analogies to the tangible, mechanical world. They did a pretty good job of this at Valparaiso (Indiana) University, which is why I now know that inductors act like masses, capacitors act like springs, and resistors act like friction (this, of course, is the basis of the analog computer, which probably doesn't exist anymore). They even took pains to point out that current running through a wire behaves remarkably like water running through a pipe, if you think of voltage as pressure, current as flow rate, and resistance as pipe friction (which is a combination of the Reynolds number and maybe some other factors which I have forgotten in the last 35 years). The point is that ALL physical systems, whether in the macro-world or the invisible, sub-atomic world, follow the same set of rules.

I can't believe there's anything really intuitive about electronics. We grow up in a world where you can start absorbing physical cause-and-effect from the first moment you open your eyes, or possibly even before birth. Electronics, on the other hand, just sits there, silent and motionless; exotic instruments are required just to observe its behavior. It's a miracle anybody can ever understand it.

"Electronics, on the other hand, just sits there, silent and motionless ..."

You've never seen a really good short-circuit, ya! Neither silent nor motionless! Check out this substation.

"It's a miracle anybody can ever understand it."

You develop a feel - an intuition about it, so to speak - and you can think of it in terms of analogies, too, like the water pipe. After many years doing electrical engineering, I can look at a fairly complex circuit and in a few minutes get a good idea of what it does and how it works - without instruments. This isn't to say I'm special in some way. Just a bit of experience and intuition mostly.

But don't let me under the hood of your car! It'll never see the road again!

Lets Make this simple shall we.

Take the Killowatt-hours the motor has run and divide by 0.7457.

That will give you the Horsepower hours.

Your conversion from watt-hours to horsepower-hours is correct. However, once the spinning mass is up to speed, running the motor longer does not contribute to the rotational kinetic energy. The OP is interested in the rotational kinetic energy. The spinning mass will still have this energy when the motor is de-energized. The mass will slow down, of course, as it dissipates its energy through friction (or usage), but once the mass is up to speed, the motor is out of the equation except for its own contribution to the total MOI.

The posters question is for an hours conversion, not an energy related to hours conversion.

Acceleration is mentioned, but nothing about the, consumption of that energy in relations to functional hours. It appears to me that no matter the speed they are looking for a direct reference to the hours use.

But I am probably wrong in my assumptions.

The OP asks for the energy (watt-hours or horsepower-hours) used to accelerate a spinning mass to some final speed, up to 2,500 RPM. Watt-hours (and HP-hours) are a measure of energy, not power. Computing the energy directly is equivalent to integrating the input power over the acceleration interval. By calculating the rotational kinetic energy of the spinning mass directly from the MOI and the RPM, the total power input (sans incidental losses) gives this result no matter how long it takes to accelerate the mass to speed. The accleration can even be erratic (so long as it's monotonic), but it doesn't matter. The final kinetic energy at speed represents the total power used to accelerate the mass, neglecting losses.

You are correct I overlooked the word used. Good thing I dont build space shuttles, just HVAC systems.

Thank you everybody. All I needed was to know how I may calculate the energy used when accelerating my mass. I understand that once my weapon is up to speed, it should take little energy to keep it there lost by friction and air resistance. So, my SolidWorks program tells me that my weapon should have an MOI of .0605 in the direction that I will be rotating it. Plugging this into our formula in Eq 4 of the second reply yields:

E_k = MOI * RPM² * 1.523087x10^-6

.0605 * 2500 RPM² *1.523087x10^-6

.5759 watt hours

The original purpose of this was to find how much battery capacity I should use by finding out how much energy it would take to spin up the weapon after every hit. We will run our motor at about 22.2 volts, so this should yield 0.5759/22.2=.0259Ah used to spin this weapon up. This seems way too small to me. Am I wrong?

If you drew 0.0259 amps at 22.2 volts for one hour to spin up the weapon during that time, you would impart roughly 2073 Joules to it at a draw of 0.575 watts from your battery. However, if you revved it up to speed in one second you'd be drawing over 93 amps at 22.2 volts (2073 watts) from your battery during that one second. So, yes, that figure sounds reasonable.

Also don't neglect losses in the motor itself when calculating your energy budget. Motor windings waste power in resistive heating. You already mentioned friction and air resistance. Your motor losses will probably be the greatest of these three.

Also note that most batteries' actual Ah capacity depends on the discharge rate. The higher the current draw, the less the battery's apparent Ah capacity. You might want to run some dynamic tests on your candidate batteries to make sure they don't wimp out on you during times of peak demand - especially toward the end of a battle. Temperature also makes a difference in how well batteries perform. Build margin in your energy budget to accommodate these considerations. We want your bot to kick bot butt, so keep us posted, won't you?

Just curious: how long do you have to spin the weapon up after a hit? If it is just a few seconds, your battery will have to supply a heavy current during that time, and it will have to supply this current repeatedly. One option you might consider is driving the motor at overvoltage to rev it up fast and then open-circuit the motor when up to speed.

Top-fuel drag racers run pure nitro in engines not really designed for the stuff. They push it all the way to the limit in exchange for rebuilding or replacing the engine frequently. They might get several thousand HP from a hemi, but only for a short time. These babies are just on the brink of blowing themselves apart, and some do.

Think of your motor as expendable; lasting only as long as it takes to win. Drive the hell out of it at higher-than-rated voltage. This also has the advantage that you needn't draw such heavy currents from your battery. They'll get hot, too, so be careful.

Do not overvoltage your motor if it is of the "brushless-DC" type. You can fry the motor's internal electronics if you do that. Use a brush-type DC motor if you aren't already. Gives you much more flexibility.

One more thing (I keep stepping out to run errands. Sorry). You might also consider using a lower-voltage motor with your 22.2 volt battery if you want to try the "overvoltage" approach. What is your present motor's voltage rating?

You could probably pick up some 6 or 12-volt motors pretty cheap. Stress-test a couple of these by revving them up, delivering your payload, and then doing it again; each time cutting the power to your motor when it's up to speed. Do this until you burn them out. It'll give you a good feel for the motor's limits of performance.

Actually, I've already ordered a very nice brushless motor. It runs at the 22.2 volts (there is a voltage cap of 24 volts in our competition) that I stated before. The motor states that it can draw as much as 100A continuously. The coolest thing is that this motor only weighs three-fourths of a pound, which is absolutely fantastic in my 15 pound class.

As for the batteries, we are almost certain that we will use lithium ion A123 batteries. This type will have a good capacity (about 2.3Ah, in a perfect world) and can supply huge amounts of amperage (70A continuous and 120A for 10 seconds).

I believe that we now have enough data to find out how long it will take my weapon to accelerate. I haven't done a stress test on the motor itself yet (because I lack the power supply necessary at this point). Therefore, I don't know how much current it may draw on normal conditions. But, just for poops and giggles, could we calculate how long it will take for an MOI of 0.0605 to accelerate to 2500 rpm under 22.2V * 100A = 2220 watts?

"... could we calculate how long it will take for an MOI of 0.0605 to accelerate to 2500 rpm under 22.2V * 100A = 2220 watts?"

Yes, but you have to make some assumptions. The most basic of these is to assume that your power input remains constant until the motor is up to speed. Under this assumption your motor will go from 0-2500 RPM in 2220/2073 seconds, or about 0.933 seconds.

The power input to the motor will probably not be constant, however, as the motor comes up to speed. How fast it actually does come up to speed in this case has a lot to do with how the motor's internal electronics manage the torque. Internally, BDC motors are really three- or four- or even six-phase motors with the internal electronics juggling the phases.

I certainly hope you have an opportunity to post footage.

I am following this closely.

I have wagered my son's tuition on your team.

RoboBots 2009 will be held at the Meadville High School gymnasium on April 4th. This is the third year of Tool City RoboBots. I am co-captain of team FreshMASH (Freshman Meadville Area Senior High School), a team that consists solely of freshman from our local high school. Last year there were 15 schools participating and thirty or so teams, and we expect to see many more this year.

Almost all of the teammates of FreshMASH fought with our bot THRESHER last year as the only all-middle school team; going up against seniors and vocational technical school students. We went 2-2 and had one of the most exciting matches of the day (is there a way to post videos?).

This year, we're using the full-body spinner design in the 15 pound weight class. Super megabyte was a very successful full-body spinner. This consists of one chassis that contains motors, batteries, and all the other guts that go into a combat robot, and a spinning weapon or shell. The shell acts as both the armor of the robot and the weapon. At this point in time, we have almost all of the parts we need and just need to drill and tap holes and put the thing together. We've teamed up with Modern Industries and Kuhn Tool and Die to have some parts CNC machined out of solid blocks of aluminum. I have some pictures below of the parts on SolidWorks and the real thing:

The chassis and shell here have been machined out of solid blocks of aluminum, except for the sides. As you can see, the sides and top of the shell are two separate parts, to conserve weight. The sides, instead of using a solid block of aluminum, have been machined out of a large aluminum pipe. You might be wondering exactly how we plan to drive our weapon. The answer is friction drive. Instead of driving the weapon off of a shaft powered by a motor and gearbox directly, we have a 3.5 hp brushless motor driving a wheel against the shell, much like how a car tire contacts the ground.

Here is the top of the shell, which will mate with the sides of the shell by interlocking tabs.

And, last but not least, are the chassis and sides of the robot. If anyone has a suggestion of how to post videos, I would really like to post some footage.

The competition was last Saturday, April 4th. My team went 4-2 and tied for fourth place out of 28 teams competing. We also won the awards for the Best Engineered Robot, Coolest Robot, and Best Sportsmanship (for hosting the event). I should be getting some videos of our fights soon. Is there any way to pose videos?

You can always upload them on youtube and post a link. I'm anxiously awaiting to see these battles!

Our local newspaper, The Meadville Tribune, created a slideshow of various pictures they took at the event. Here is the link. Slides 13 through 24 all feature our team and robot, and my hands are in slide 26.

The team captain's sister took videos of every one of our fights; once they upload them onto youtube I'll paste the links here. It was quite destructive.

Here are the links to the videos on youtube. The link is to our team's channel.

http://www.youtube.com/user/MASHrobotics

What will the force be when the other bot receives a whack from the sledge hammer?