> Would it be ethically wrong to recruit an undergrad for a few days
> volunteer work without pay to get the computer crunching part done and
> not mention him as a coauthor and only mention as acknowledgement?

It's not ethically wrong **if** the engineering contribution is too tiny, compared to the whole contribution of the paper.

In fact, it's very common that professors/researchers hire several undergrads/interns to work on engineering a tool, and only list them in the acknowledgment. (I can provide many examples).

However, it is ethically wrong if the engineering contribution is substantial, and you don't list them as co-author. Whether there contribution is enough for co-authorship depends on your judgement, but your judgement can be wrong.

If you read the book "7 habits of highly effective people", one of the habit is always thinking about win-win solution. You can just expect somebody to work for you for free. It sounds unrealistic.