Have your toad push your motorhome (grade assist)

[davidbrady]

This is a topic that comes up every now and then. Its feasibility has always been quickly dismissed. This morning I took a couple minutes to scratch on the back of an envelop. Here's what I found:

A common argument against PUSH (or toad assist on grades) is that the typical tow bar isn't designed for it. Everyone knows that tow bars are designed for towing and not pushing. (Here I don't say anything about any particular bar. I simply draw some generic conclusions that can be applied to any bar).

One of the forces that tow bars need to resist is braking. When the bus driver applies his brakes the toad is forced up against the bus. In effect and in the absence of toad auxiliary braking the toad is pushing the bus.

A typical bus should be able to stop from 60 mph in 200 ft. This equates to a deceleration rate of (Deceleration = VelocityInitial**2/(2*Distance)), or 20 feet per second squared.

I chose the toad weight to be 5000 lbs which seems to be a good estimate for the average toad.

As the bus decelerates the toad exerts a force on the bus thru the tow bar. With a toad weight of 5000 lbs and a deceleration rate of 20 feet/sq sec, the force the toad applies to the bus is (Force = mass*deceleration) or 3060 lbs. So in fact, the tow bar needs to be designed to handle significant forces under panic braking.

Now, with my 2002 LXi I know that I require 500 HP to climb a 6% grade at 50 mph. Remember that not all of my crankshaft horsepower is applied to the wheels; there are losses along the way and those losses are typically in the range of 20 to 30%. Let's assume that 75% (or .75*500 = 375 HP) of the crankshaft HP appears at the wheel.

Let's see what kind of horsepower the toad is exerting on the bus during panic braking.

The formula to convert tractive force to horsepower is P = F*S/375 where F is the force exerted by the toad, S is the speed at which the force is exerted, and P is horsepower. Substituting in F=3060 lb, S=50 mph we get 408 HP. Notice how this number meshes well with my 375 HP prediction based on experience. Also notice that we're not applying more force to the tow bar than what would normally occur in an extreme stop.

It's likely that your toad isn't capable of 400 HP at the wheels. It may be that you're only capable of 200 wheel HP. This reduction in HP and it's associated reduction in tractive force means that you'll be applying even less force to the tow bar than what it will see in a panic stop.

What this quick back-of-the-envelop shows is that there's promise in PUSH assist.

Disclaimer: This is a simple physics brainteaser and is far from exhaustive. Lots of real world corrections, factors, and safety practices need to be addressed. I don't recommend anyone push their motorhome due to these issues. In addition there are State laws and DOT statutes to comply with. What this simple analysis shows is that as a campfire discussion the idea can be kicked around some more!