Gear Calculations.

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I am trying to work out gear ratios when used with a worm foe model railway use. They usually work out at a ratio like 40:1 or a figure that looks like that (E.g. 25:1 or 60:1 etc).

The problwm is when I try to work it out the official ways via looking on the internet I seem to get odd figures like 4.25 which no way would it end up being 4.25 to 1 (4.25:1) with the number of teeth it has on the cog and worm. It should be giving me a high figure.

Does anyone know the way to calculate these things?

I can count the number of teeth on the cog and the number of windings on the worm and the diameter of these etc.

I realize the pitch also effects things a little but I have no info. about the pitch other then a picture and the business selling them will not know.

All I want is a simplified formula to give me a rough idea.

Now as the cog part can't be any larger then the wheels it turns I can not go larger then this, or the cog will end up hitting the track.

My aim is to reduce the model locomotives top speed by changing the gearing, and I also aim at getting something rather nice at the same time. I have the equipment to enlarge the hole centres in the cogs or worm if needed as long as the holes are not larger then the axle and motor shaft, then I am ok. (Usually the other way round).

I will habe a look at other internet advice on gear calculations. If it was a cog to cog situation, even if they were 45 degree angles, it would be easy, but the worm part has thrown mw in my thought as to how to estimate it. (I do not need a 100% accurate formula. Just a simplified idea so I have a rough idea if these worms and cogs will actually reduce the gearing on my model and by how much).

I have found the answer though I do need a clarification on double start worms. Does one halve or double the end result compared to if one made a calculation for a single start worm if that makes sense?

Why can't the ratio be 17:4? Are there fewer than 4 teeth on the one gear? Does 4.25:1 seem too low, or is there something I'm missing?

To work it out with a single start worm it is a lot easier then I had thought.

Count the number of teeth on the cog.

So 40 teeth gives you a 40:1 gear ratio... So in the case of model railway locomotives where the worm is mounted to the shaft of the motor, the motor in this case will need to turn 40 times to give one revolution of the wheels.

It is not possible to have a result of a figure after the decimal point. Also, I doubt it is practical to make a cog with less then about six teeth.

What I don't know yet is how double start worms are calculated where there is a double thread winding on the worm. I know the answer is either half or it is double the amount then if it was a single start worm. I am not sure which it will be as yet. I imagine it will be double.