KE vs MOI in Spinning Weapons - Amateur
- Adam Wrigley
Last updated - June 2006
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KE vs MOI
When designing a weapon, the first thing that comes to mind is making it have the most kinetic energy. At first pass, it seems that more KE will make more damage. Most people also say that having a good "MOI" is key to success. MOI is the Mass Moment of Inertia, it works like a mass does in linear systems, but for rotational systems. While more KE has the potential to do more damage, and more MOI can store more damage per RPM, one must look slightly farther to figure out how to make an efficient spinning weapon.
First thing first, doing damage does not necessarily mean you will be damaging the other robot, you could also damage yourself. The first step in designing any spinning weapon is to make sure that your weapon will be able to withstand its own hits. This step is tricky, since the forces generated in an impact are nearly impossible to figure out in advance. You'll have to exercise some common sense here. Don't make your weapon too light, too flimsy, too thin. If you have any doubts about your weapon's construction, it's probably too weak. Make it stronger than you think it needs to be, because that probably still won't be enough.
Now, of course you can make many different sizes of sturdy weapons, how big should it be? Should you build a lightweight, 20,000 rpm spinner? Or should you build a heavier 2000 rpm one? This is a game of optimization. The heavier your weapon, the less weight you have for the weapon drive system. The heavier the drive system, the less weight you have for the spinner. One advantage of MOI however, is that you can increase MOI without increasing mass. By moving the weight of your spinner closer to the perimeter of the weapon, you will increase it's MOI. However, more MOI will take longer to spin up.
We have to take a closer look at what is going on with the weapon drive system. Generally, spinning weapons are powered by electric motors and batteries. Your batteries will source all the power to spin your weapon. Because of this, all your KE that you put into the disc, is initially stored in the batteries as potential energy. If your batteries don't have enough PE, you won't get the KE you want. The other link is the motors. The motors transfer the battery's PE to the weapon's KE. The motors will determine how fast you can put that PE into your disc. Bigger motors will do the job faster, smaller motors will take more time. Batteries also play a role, as they can only source so much current at once, which controls the rate of energy transfer. In the end, if you have the same weapon drive system, no matter what the MOI of your weapon is, you should be able to get the same KE in the same amount of time, by tweaking your gear ratios.
However, there is yet another factor here, wind resistance. When spinning a bar at 200 mph + there is considerable wind resistance on the blade. This causes less energy to be put into the weapon's kinetic power, and more towards keeping the weapon at speed. If you have a heavier bar spinning at 100 mph, you will have a much more efficient system, and more energy in the bar.
This is yet another game of optimization, how much MOI can you put in your weapon, before it becomes too slow. You may have a lot of energy in your weapon, but if it is moving too slowly and simply pushes opponents out of the way, then this is no good. You want to tear into an opponent and do damage, and this will require tip speed and contact.
# of Teeth
The largest factor to consider however, is how you'll be hitting the opponent. How many teeth are on your robot's weapon, and what shape are they? What is important is to take into account how much of the tooth will come in contact with the opponent on a hit. If you imagine looking at your robot's weapon spinning, you can imagine the teeth going by. As the number of teeth on your weapon increases, the time between you seeing a tooth decreases. The teeth are going by faster and faster. Now imagine another robot trying to hit you. In the collision, the other robot will have to sneak by the tail end of one tooth as it goes by, go forwards, and then get hit by the next tooth. If you have too many teeth, or you are spinning too fast, then the teeth cannot get enough contact on the opponent in this small amount of time and you will simply bounce off of the opponent's frame. Here is a simple formula that will calculate how much of your tooth will contact the opponent:
{60/[RPM * (# of teeth)]}*(total speed of colliding robots)*12
Javascript Calculator:
Keep in mind this is the optimum case, so actual tooth contact will normally be smaller than this. Average tooth contact will be about half of this number.The total speed of colliding robots is the speed of your robot, added to the speed of the robot hitting you, in feet per second. The result of this equation will be the amount of tooth that will contact the opponent, in inches. A good estimate for the total speed of colliding robots during a spinner collision is 20 FPS in classes 30 lbs and above.
# of teeth refers to how many protrusions you can see around the perimeter of your weapon, while looking down at an axis perpendicular to it. For example, a bar will have 2 "teeth." A shell spinner that has 6 teeth total, arranged with the teeth stacked in pairs around the perimeter, is said in this case to have 3 "teeth."
There are two general types of spinners in robotic combat. The big hit spinner, and the "many little hits" spinner. If you want a big hit, you'll want to use few teeth, generally 3 or less. This will allow for maximum tooth contact per hit. If you want lots of smaller hits, more teeth will be better because it will minimize the amount of tooth contact per hit.
Tooth Design
The actual shape of the tooth is one of the most important parts of your design. Do you want one big hit, or lots of little hits? In the above picture Tooth 1 has what is called a positive rake while Tooth 2 has a negative rake. In machining, negative rakes are used to fine tune designs and get the machining precise, while positive rakes will take out a lot of material fast, and not too accurately. If you want big hits, use a design similar to Tooth 1, if you want many smaller hits, use a design similar to Tooth 2.
Summary
In the end, you need to take all these topics into consideration when deciding how fast to make your spinner, and how much MOI to give it. You need to make sure your weapons is strong enough to take its own hits, it does not spin so fast that wind resistance is seriously affecting it, you can actually get some good contact on your tooth, and the tooth can deal damage when it gets that contact. If you can't hit your opponent with your devastating kinetic energy, then it's pointless to have all that KE in the first place.
As a last concern, you'll need to make sure you can spin your weapon up in a reasonable amount of time. You don't want to have a great weapon system that takes 30 seconds to spin up. Click here for our spin up time calculator.
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