As a Captain on the older B-737–200, before we had computerized flight mgt systems, I made a math error on a descent profile. We were able to do the math in our heads, which worked out ok, usually.
We were coming into Columbus, Ohio. I forget the exact error, but here is how it works:
You are at FL250, when you receive ATC instructions to cross “Point Xray” at 11,000 ft and 250 knots. So you repeat the clearance verbatim, so that ATC knows you heard it correctly. In this case, NORMALLY. I’d do the calculation in my head, then check with my FO to hear if he/she agreed with my math. For some reason, I got distracted, I was tired, whatever – I didn’t do it.
In this scenario, you subtract 25 – 11. The answer is 14. Multiply that by 3 = 42, So, for every mile vertically in the descent, you cover 3 miles horizontally. We called it a 3:1 descent. So, I would begin our descent 42 miles from “Point Xray”. It’s a 3:1 descent. Due to the airspeed (depending on the winds), I’d add another 5 miles. So 47 ,miles from Point Xray, I SHOULD have pulled the plug and initiated our descent at 2,500 FPM
Well, apparently, my math was off by 10–15 MILES! That made us high. Suddenly, my FO asked, with concern in his voice: “Hey!. Are we going to make this?” The next second ATC queried: “Have you begun your descent, yet, sir?’ THEN the light came on in my brain! Embarrassed, I apologized, admitted my error, and requested a left 270 to lose altitude and get back on profile, which was approved.
It never happened again. I could have caused a traffic conflict. Well, maybe my FO could have prompted me a little sooner – maybe a little CRM breakdown there. However, I could have precluded that, if I had briefed him on my planned descent to get him “in the loop” earlier. Then, when he saw me sitting there fat, dumb, and happy at 47 miles out – not descending – he’d say something.