We at PVEng use hand calculations when we do not have a program or spreadsheet or when we want to create a spreadsheet and need verification. Hand calculations are respected more than programs for audits or code submission but in my opinion, they are much more likely to be wrong.
The ideas presented here are designed to reduce the most common causes of hand calculation problems:
These common problems will be investigated in more depth on the following pages.
Without references it is not possible to check if the equations are sourced right.
The correct equation is t = PR/(2SE+0.4P) not as shown above. With the references listed it is possible to go back and find this copying problem.
The illustrated intermediate step allows the reviewer to see what numbers were used for the variables. It is not possible to check what is not known.
How was the first answer calculated? What values were used for P,R,S and E -why is the first answer wrong?
Here we are assuming that the reader/reviewer understands what P, R, S and E mean, probably a good assumption. However, it would be a better assumption if the reference for the equation was included. There is no reason to provide further explanation for something that is easily looked up.
The equation should read specific gravity, not density. Without the units, it is not verifiable.