Gear Ratios, Torque, and Speed

Hello!
Recently, I was in a solar car competition (in school). My group made a car with a wooden frame, two big wheels on the back, and two small wheels on the front. There were certain rules to the competition. We used a "solar motor". We attached a small gear to the axel of the back wheels, and a large gear to the motor. The gear ration was approximately 4:1. We used a reletively small solar panel, that produced 1.7V in the sunlight when we tested our car. When we put placed our car in the sunlight, the motor can spin without any load. But, once we placed the gears together, the motor would not turn. We pulled the wheel axel down, and the motor spun again. There was not that much resistance between the gears, as we could feel. Someone in the group loosened the contacts between the gears, and the wheels began to slowly spin when off the ground. The gear ratio should make the wheel spin very fast. But, there is something I don't get about gear ratios: you can't make new energy out of nowhere; something must be sacrificed. A 4:1 gear ratio should make the small gear spin 4 times the speed of the big gear. Is torque sacrificed? What is torque anyway? I think that it is the pulling force. But, something moving very fast seems to have lots of force (the regular motor), but still isn't strong enough. But, slower spinning servo motors are very strong; maybe even stronger than the regular motors. Is the solar car lacking torque? Can someone describe to me what torque is, and how torque and speed relate to each other? Why is a small gear ratio (e.g. 1:4) ever needed, and how can it have an advantage? I have a R/C helicopter with a very small gear spinning a larger gear. Most people think a large gear ratio is always perferable. Big gear ratios vs. small gear ratios? Yes, I searched on Google!
Thanks!

Is torque sacrificed?

Yes.

What is torque anyway?

The turning force. Think of it as the value of force you would have to apply to exactly stop the motor from turning.
When a motor first starts up it must provide enough torque to overcome the inertia of what it is attached to. Then once it is turning it only has to supply enough torque to overcome the friction in the bearings.

and how torque and speed relate to each other?

In general they don't they are two independent measures of a motor's performance. However with gears the increase in speed to a certain ratio is accompanied by the increase in torque by the same ratio.

I have a R/C helicopter with a very small gear spinning a larger gear.

So that is converting some of the speed into more torque.

If a motor is specified at, for example, 10 oz-in of torque, that means it can provide 10 ounces of force at 1 inch from the center of rotation. If you increase or decrease the distance from the center of rotation you similarly decrease or increase (inverse) the amount of force. E.g., if you double the distance from the center of rotation you halve the force available. Torque = Force * distance. Torque is something of a yes or no question: if I have enough torque I can move it and if I don't I can't. In the case of your car you didn't have enough torque so it just didn't move.

Your helicopter uses gear reduction for two reasons: first because the propeller is aerodynamically limited to how quickly it can spin (before it starts to "stall" -- that's out of scope here ;), and secondly to gain more torque. Assuming stall was not an issue, without the gear reduction the propeller would spin up to a certain RPM then not increase any speed because the amount of torque it can provide at that speed will limit it from pushing the blades more quickly.

Why use gear reduction at all -- why not just use a motor with more torque? The issue is that building an electric motor with more torque requires a physically wider motor with more poles and thus it becomes more expensive. It turns out that it's cheaper to produce the motor to spin more quickly and then use gear reduction to gain the torque.

Chagrin:
...it can provide 10 ounces of force...

Force = Mass * Acceleration. So how can you express force as mass?

Chagrin:
...why not just use a motor with more torque?

I have to use the "solar motor" they provide. No, they don't have the specifications.
The car might actually have spun if we did gear reduction. Only one team in the school actually got the car to move on the table and move to the next level of the competition. They (teacher) ignored all the other teams' cars and did not test them. He just came in and said, "There is already a winner from the other class, so the competition is over now." However, a team in my class actually made the car go slowly on the table by attaching the motor directly on the axel. Everyone blamed the motors / solar panel.

dkl65:

Chagrin:
...it can provide 10 ounces of force...

Force = Mass * Acceleration. So how can you express force as mass?

In everyday language we blur the difference between mass and weight (weight = mass * acceleration due to gravity). I could have described the torque of the motor in Newtons but that would just makes things harder to grasp.

The "why not use a motor with more torque?" question was intended to be rhetorical. I was anticipating that you'd ask why your helicopter was using gear reduction when it could just use a different (slower, with more torque) motor instead.

A pound-force is a unit in its own right, being the force exerted on the mass of a pound under "normal" gravity. So an ounce-force, which is what was implied above, is a legitimate way of measuring force, as opposed to being a mass.

(But I do prefer the metric system where kilograms are mass, and Newtons are force and there's no scope for confusion. It's easy to visualise too, since if we take gravity as 10 (rounded up from 9.81) then an apple of mass 100g has a weight of 1N (appropriately enough!) and a 100kg rugby player has a weight of 1kN.)

We attached a small gear to the axel of the back wheels, and a large gear to the motor. The gear ration was approximately 4:1.

You really should have gone the other way. If you look at any sort of motor driven vehicle (of practically any scale), you will see a gear reduction drive between the motor and wheels.

Torque is increased/decreased proportionately with gearing. With a 4:1 gear multiplier, you decrease torque at the wheels by 1/4th. If you had gone with a 4:1 gear reduction though, you would have increased torque at the wheels by 4x (or rather, 8x of what your gear multiplier was providing).

something moving very fast seems to have lots of force (the regular motor)

It takes very little force to accelerate a small mass up to a high speed (the mass being the rotor of a motor, for example), so the freerun speed of a small motor is really not much of an indicator of it's torque rating. That freerun speed can be an indicator of how much gear reduction you can utilize to increase it's available torque output to the wheels though. That increase in torque will come with a lower top speed of the vehicle though, which is where the tradeoff exists. Of course, the torque has to at least overcome the internal frictions of the drivetrain to attain any speed at all, as you've already experienced. Beyond that, your gearing is a balance of top speed vs acceleration (ignoring aerodynamic drag for the time being).

Force = Mass * Acceleration. So how can you express force as mass?

It's a simple algebraic manipulation of the formula.

f=m*a
m=f/a
a=f/m

Of course, the application to a real world device isn't quite as simple, but the formulas do provide a clear view of the relationships between force, mass, and acceleration. IE, if you double the mass, then your acceleration is cut in half, or you need twice as much force to maintain a given acceleration. Of course, once the various frictions come into play, things get more complicated.

With a 4:1 gear multiplier, you decrease torque at the wheels by 1/4th.

You reduce torque to one quarter, surely?
"by 1/4th" suggests you've still got 75% of the torque you started with.

Last year, I saw a Lego crane with gear reduction. I asked the teach why they used a small gear ratio instead of a large one. The teacher said that it is used to gain torque. I should have told the group to use gear reduction, and explain to them why.

So, if I put a paper towel tube on a bathroom scale, pushed down until that scale read 10kg [or until it breaks], I am putting 10kg of mass on top of the tube, or 98.1N of force.

If a 1000kg car moves steadily at 20km/h hits a 45kg person standing still, how much force does the car hit with, and how much mass is exerted on the person?

and how much mass is exerted on the person?

You can't "exert" mass.
Mass is the amount of stuff an object contains.

If a 1000kg car moves steadily at 20km/h hits a 45kg person standing still, how much force does the car hit with

Such collisions are very, very inelastic.
The car has about 15.5kJ of kinetic energy, but how much is transferred to the person is extremely difficult to calculate.
The car itself is designed to deform and absorb some of the impact, and where the person struck with respect to their centre of mass also has a bearing on the outcome.

Edit: Cars really are overkill.
I was just looking at the Wikipedia page for the Claymore mine, where part of the specification says that an impact of only 79 Joules (albeit delivered by a fast-moving, sharp and hot lump of metal) is sufficient to deliver a lethal injury.
{ER voice} "Charging 200 Joules - stand clear!" {/ER voice}

Servos are strong motors. I wished that all servos are continuous rotation. That way, the Servo library can set the servo to 0-359 degrees. There would be a function that rotates the servo 195 degrees, etc. CW or CCW, a function that rotates the servo 3 full rotations, etc, and a function that continuously rotates the servo CW of CCW until a stop function is called. Why couldn't they make all servos capable of full rotation?

Because it's really hard to make potentiometers like that.
Anything other than pots are expensive.

Anything other than pots are expensive.

Just look at how expensive the pots are:-

Servos have potentiometers inside them? How does the pot relate to the motion of the servo (how does the servo work)?

Servos have potentiometers inside them?

Yes.

How does the pot relate to the motion of the servo

The motor moves the pot and the value of the pot indicates the position of the motor. The electronics compares the current position of the motor with the required position and moves the motor accordingly.

A continuous rotation servo is an oxymoron, once it is continuous rotation it is no longer a servo. However many people use the term to mean a bastardised servo where you can control the speed by giving it a spurious angle to turn to.

A continuous rotation servo is an oxymoron, once it is continuous rotation it is no longer a servo

Not strictly true - "servo" is a specific term, adopted loosely by the R/C community.
An R/C servo adapted for continuous rotation is no longer a servo.

However, devices capable of continuous rotation and possessing the ability to rotate to a given position exist.
In general, they're not cheap, certainly not the sub $10 range.

AWOL:
In general, they're not cheap, certainly not the sub $10 range.

I see regular servos in Sayal that cost >$10.

AWOL:
An R/C servo adapted for continuous rotation is no longer a servo.

Then what should we call those things?

I see regular servos in Sayal that cost >$10.

So?
Metal geared R/C servos are very much more than that, but they're still cheap compared to industrial servo systems.

Then what should we call those things?

In the spirit of the Dead Parrot Sketch, I refer to them as ex-servos.
They have ceased to be.