# Physics of Trailer Hitch Height

I'm modifying a lawn tractor to pull single axle trailers in a woodland environment. They are rear wheel drive, have enough power, but traction is our biggest issue even when using tractor/ATV tyres.

My question is - what height (in relation to the rear axle) should the tow hitch be at and why?

I have looked at tractor pulling for comparisons and

• they seem to go as high as they can within the rules but I understand this is due to benefits of lifting the front of the sled off the ground.

• they extend the hitch to influence front wheel lift - I guess this is to put more weight on the back axle.

Front wheels lifting on woodland slopes isn't ideal so I have always opted to go low (below axle line) as this pulls the front down and I don't see how it could reduce the weight on the back wheels.

But a physics explanation would be really helpful.

EDIT: I also found these two links which undertake a complex analysis of sled pulling with trucks under the title 'Physics of a truck pull, using a 2WD pickup truck'.

Thanks.

• If you can show that going low pulls the front down, then the same logic will show that it reduces the weight on the rear wheels... – Solar Mike Jan 14 '19 at 17:28
• Interesting thought @solarmike. So would it make more sense if I said it lessened the effect of the front lifting because the tractor was more able to drive out from under the hitch? – Davies-Barnard Jan 14 '19 at 17:36
• Is it easier to push or pull a wheelbarrow? Think about drawing how the forces are applied. – Solar Mike Jan 14 '19 at 17:37
• I think I need to do exactly that this evening. – Davies-Barnard Jan 14 '19 at 17:41
• @alephzero. Interesting idea. There isn't a lot of space under there. Currently reading a couple of PDFs found on JimHawley.ca – Davies-Barnard Jan 14 '19 at 20:01

Let's say you need to tow 1000kg weight. And you have your hitch at 10 cm, 01meters above the axel of your tractor.

If you pull it with an acceleration of 2 meters per second or 1/5 g. You have an overturning torque trying to lift up the front wheels of

$$1000*2*0.1= 200 *9.8 Nm.$$

This is enough torque to lift the front wheel of a small garden tractor. If you put the connection lower than axel you loose part of traction due to the redistribution of part of the mass to front wheels.

So may be best is to hook the trailer hitch lined up with axel or barely above it.

• Thanks @Kamran. We have recently modified the tractors (ATV Winch and larger battery) to give us more weight on the front. So maybe with this additional weight the front popping will be less of an issue and we can now focus on getting trailer weight onto the rear axle. – Davies-Barnard Jan 15 '19 at 8:13
• @Davies-Barnard why do you think trucks have the 5th wheel coupling? – Solar Mike Jan 15 '19 at 9:02
• @SolarMike to get the weight over the wheels - I see that - but to counter claim why do tractors have their tow/pickups so low? – Davies-Barnard Jan 15 '19 at 11:29
• @Davies-Barnard To keep their front wheels on the ground ie to avoid the very issue you are having... !! – Solar Mike Jan 15 '19 at 12:04