So....some of the best minds in Science (or as we call it at LosAlamos...SCIENCE) frittered away almost an hour of time this morning working this problem.

Most of them were unaware that Fri was ENIAC Day. Just no sense of history, I guess.

The ENIAC was developed for/funded by the USArmy to calculate artillery firing tables. I got to thinking about this problem this weekend & it was driving me crazy. Why would you need the ENIAC for such a simple calculation??

You are given a (presumably non-moving, a moving target would complicate the problem..but only slightly) target X miles away. You have an artillery shell that weighs W pounds. You load the cannon (not the Pacabel one, though) with enough HE (High Explosive) to put J joules of energy into the shell. What angle A do you aim your cannon to hit the target X miles away??

If you assume a point artillery shell (like we sometimes assume a spherical cow for certain purposes), the arc will describe a parabola under the Earth's gravitational field. That trajectory requires only the mere solution of a quadratic equation that you can do with a slide rule (Post or K&E are the slide rules of choice). Why would you need an ENIAC for a back-of-the-envelope calculation??

However, an artillery shell is not a point. It is a projectile that has a volume and, therefore, there is air-resistance during its flight to include in the calculation. There is also the air temperature/density that affects the air resistance, so the coefficient of friction varies. To correctly do this calculation of angle A requires the solution of a differential equation. Usually a Runge-Kutta numerical solution of this time-dependent differential equation. Hence, the need for the ENIAC. Since artillery commanders are not skilled in solutions of differential equations and have no ENIAC at their side, they need a set of tables to determine the firing angle A. So this was what the ENIAC was designed to provide the USArmy.

This group of high-level scientific types decided that in less than an hour, we could write an iPhone app that would do this calculation for these artillery commanders and free them from hauling those ENIAC-generated tables around with them out in the field. We plan to sell it for big $$'s to the USArmy.

And you all thought we had bigger problems to solve at LosAlamos!!

Tom

*Edited by TomHill (03-18-2019 10:38:39)*