[JVN]

Originally Posted by Joe Johnson

I admit that the qualifications of A and B went past me upon first reading. Given those qualifications, then I agree, there is no reason to have BOTH multiple motors and shifters.

Joe J.

Disclaimer: Beware this post... actual math may be involved!

Allright... I'm going to have to humbly disagree, and challenge this statement.

When I read this... it essentially shattered my little "shifting is necessary" paradigm, and it scared me enough that I actually decided to check the numbers. (School is out... I actually have time to run some numbers!) So... let's walk through the calculations I did, and see the results. Does the above statement hold up?

Sorry Joe, Sorry Matt... my numbers say you are both wrong.

The 3 major factors here are:
1. 10 fps max speed
2. 150 lb linear bot pushing force
3. 4 Motors, no shifter.

First off... Set up some assumptions:
I'm gonna say, let's be nice. I'll assume 100% efficiency for the whole gearbox, (cuz I'm a nice guy so I'll break the laws of physics for you gentleman ). Notice, I'm also using the SLOWEST "competitive max speed" you mentioned (10fps). I'll also design to achieve this at the motor's free speed (again, cuz I'm a nice guy... and we'll assume no speed loss anywhere in the gearbox).

What does this mean?

Basically... I'm giving Joe and Matt the benefit of the doubt. I'm setting things up so they are COMPLETELY in Matt/Joe's favor. I WANT to prove myself wrong.



So, let's begin...
First, we'll design our combiner.

I'm going to use the Drill and the Chip, the 2 most powerful motors in our kit (again, just to be mean to myself, and nice to Matt/Joe). I design to match free speeds at 3688 RPM. (A 15:80 reduction off the Drill, and a 12:18 reduction off the Chip... gives us about a 99% speed match). I'm happy.
Based on my combiner theory this means the new "super motor" has a stall torque of 7.97N*m, a stall current of 234 Amps, and a free speed of 3688RPM. All of this is done at 12V for both motors.



Now, let's find our "10fps" ratio.

I'm going to choose a 6" dia wheel, simply because it's common. If we want our robot to go 10 feet per second, using a 6" wheel the wheel needs to be spinning at about 382 RPM. Now, we know our "super motor" free speed is 3688 RPM, so what reduction do we need between the motor and the wheel?
(382/3688 = .104).
So, we'll use this as our gearbox reduction.



Now... let's see what kinda max torque our new box is capable of.

Our "super motor" stall torque is 7.97N*m, which means (1 side of) our robot has a stall torque of (7.97 / .104 = 76.63 N*m), again with a 6"dia wheel, this is about 113 lbs of linear pushing force. Using 2 gearboxes this yields 226 lbs of pushing force (at stall). So yes... your gearbox has fulfilled the design requirement of 150lbs. However... the super motor is at stall, and drawing 234 Amps... which is bad.
I'm not happy with it, are you? Let's see how bad it is.



So, let's see what kinda current our robot draws if it's pushing 150 lbs.

150/2 = 75 lbs per gearbox. Using a 6" wheel we can see that we need 50.84 N*m of output torque from each box to achieve 150lbs of linear pushing force. To calculate the torque load on our "super motor" we simply say: 50.84 *.104 = 5.287 N*m. Now... how will our super motor perform under a 5.287N*m load? Well... by distributing the load, and calculating, I show that the Drill Motor is drawing 85.09 Amps, and the Chiaphua is drawing 71.76 Amps. These values are unacceptable for our competition. You'd burn up breakers if you tried to push for any extended amount of time (which is often necessary).

Simple solution to this?
Add a shifter to your robot.


Okay Joe/Matt... am I missing something?
I come from the "shifting side of the tracks" and am a huge fan of using a shifter to solve all my drivetrain problems. I'm also super-conservative when it comes to motor loading, and I always worry I'm going to draw too much current.

Based on my calculations, your above statement is wrong.
If you want to achieve Matt's "competitive speed" and his "competitive pushing force" in the same bot, using only 4 motors... you NEED a shifter. Otherwise... you're going to pop the breaker and sit there dead the whole match.

Prove me wrong...
John (who sometimes has issues with arithmatic and algebra)


PS - I want to emphasize this was all in good fun, and in the interest of learning. Can anyone show me if I went wrong somewhere?

Man.. this was fun! A real live enginerding debate on CD that involves... *gasp* NUMBERS!