How to Figure Out Equation for Foot Pounds of Force

Are you going to litigate? If so, nothing you get here will be admissible as evidence.

There are many assumptions to be made, some very significant.

The future defendant's size is not too significant. It's more about how much force he was able to produce as he drove the tamping bar into the ground.

How far the bar sank into the ground is dependent on soil composition etc. How far it drove your foot into the ground might be more relevant. Surface area of foot vs surface area of tamper.

You size and weight are irrelevant.

You'd need to reproduce the force/acceleration of the bar, at least. Not with your foot as the target. You might rent a force gauge and ask the guy to take a few shots at it and record the pounds generated as a start.

I'm a little confused.

Whatever you do, please use correct units. Foot-pounds are not a unit of force; they are a unit of energy. I'm not sure how the number would be relevant, anyway, and instead would simply focus on actual identifiable damage to your foot. How did it get into the path of the bar, anyway?

The best we can say, given the limited info, is "not much... there we no bones broken." Probably the peak force was less than 1000 lbs.

Even a very rough answer would require the soil specs, the shoe specs, the foot elasticity in the area subject to impact, video of the compacting process to assess the bar velocity, the end area of the bar, etc.

You could instrument the bar and do trials, with your foot under the bar. Measure bar deceleration rate to get a peak force. Perhaps you could use a cell phone duct taped to the bar... there's an app for that.

Less accurate would be a shoe with a foot-like but inanimate object inside: perhaps some raw baby back ribs.

As a rough guide, the steel toe cap in an industrial safety boot will sustain an impact of a little over 20kg dropped from 1 metre, or a carefully-placed load of about 300kg, without transferring any part of the load to the foot it protects.