# Quirks in ideal time calculations

Updated on 20th June, 2013 with “Method IV”.

Consider this speed chart:

Begin (km) End (km) Speed (kmph)
0.00 5.00 31
5.00 10.00 29
10.00 15.00 17

And now the question: if you were to start driving at 00:00:00, what times should you be at the 4.32, 9.05 and 13.93 km marks? Simple, right?

Apprently not!

Different rally organizers have different ways of calculating ideal times. We have discovered 4 of these:

Method I
Don’t discard any fractions in the intermediate steps, round up the seconds at the end.

Method II
Don’t discard any fractions in the intermediate steps, but truncate the seconds at the end.

Method III
Calculate ideal times for each speed sector separately, discard fractions of seconds at each sector, truncate the seconds at the end.

Method IV
Calculate ideal times for each speed sector separately, round up fractions of seconds at each sector, round up the seconds at the end.

Sounds confusing just writing it! Let’s try and see if we can figure this out by answering the question using each of these methods.

4.32
Method I
Time = (4.32 – 0.00) / 31 = 0.139354839 hours
0.139354839 hours = 0.139354839 * 60 minutes = 8.36129034 minutes
0.36129034 minutes = 0.36129034 * 60 seconds = 21.677420 seconds
Rounding up, ideal time at 4.32 = 00:08:22

Method II
Time = (4.32 – 0.00) / 31 = 0.139354839 hours
0.139354839 hours = 0.139354839 * 60 minutes = 8.36129034 minutes
0.36129034 minutes = 0.36129034 * 60 seconds = 21.677420 seconds
Truncating, ideal time at 4.32 = 00:08:21

Method III
(4.32 is in the 1st speed sector)
Time = (4.32 – 0.00) / 31 = 0.139354839 hours
0.139354839 hours = 0.139354839 * 60 minutes = 8.36129034 minutes
0.36129034 minutes = 0.36129034 * 60 seconds = 21.677420 seconds
Truncating, ideal time at 4.32 = 00:08:21

Method IV
(4.32 is in the 1st speed sector)
Time = (4.32 – 0.00) / 31 = 0.139354839 hours
0.139354839 hours = 0.139354839 * 60 minutes = 8.36129034 minutes
0.36129034 minutes = 0.36129034 * 60 seconds = 21.677420 seconds
Rounding up, ideal time at 4.32 = 00:08:22

9.05
Method I
Time = (5.00 – 0.00) / 31 + (9.05 – 5.00) / 29 = 0.300945495 hours
0.300945495 hours = 0.300945495 * 60 minutes = 18.0567297 minutes
0.0567297 minutes = 0.0567297 * 60 seconds = 3.403782 seconds
Rounding up, ideal time at 9.05 = 00:18:03

Method II
Time = (5.00 – 0.00) / 31 + (9.05 – 5.00) / 29 = 0.300945495 hours
0.300945495 hours = 0.300945495 * 60 minutes = 18.0567297 minutes
0.0567297 minutes = 0.0567297 * 60 seconds = 3.403782 seconds
Truncating, ideal time at 9.05 = 00:18:03

Method III
9.05 is in the 2nd speed sector
Time to complete 1st speed sector = (5.00 – 0.00) / 31 = 0.161290323 hours
0.161290323 hours = 0.161290323 * 60 minutes = 9.67741938 minutes
0.67741938 minutes = 0.67741938 * 60 seconds = 40.6451628 seconds
Truncating, ideal time at end of 1st speed sector = 00:09:40

Time at 9.05 = 00:09:40 + (9.05 – 5.00) / 29 = 00:09:40 + 0.139655172 hours
0.139655172 hours = 0.139655172 * 60 minutes = 8.37931032 minutes
0.37931032 minutes = 0.37931032 * 60 seconds = 22.7586192 seconds
Truncating, ideal time at 9.05 = 00:09:40 + 00:08:22 = 00:18:02

Method IV
9.05 is in the 2nd speed sector
Time to complete 1st speed sector = (5.00 – 0.00) / 31 = 0.161290323 hours
0.161290323 hours = 0.161290323 * 60 minutes = 9.67741938 minutes
0.67741938 minutes = 0.67741938 * 60 seconds = 40.6451628 seconds
Rounding up, ideal time at end of 1st speed sector = 00:09:41

Time at 9.05 = 00:09:41 + (9.05 – 5.00) / 29 = 00:09:41 + 0.139655172 hours
0.139655172 hours = 0.139655172 * 60 minutes = 8.37931032 minutes
0.37931032 minutes = 0.37931032 * 60 seconds = 22.7586192 seconds
Rounding up, ideal time at 9.05 = 00:09:41 + 00:08:23 = 00:18:04

13.93
Method I
Time = (5.00 – 0.00) / 31 + (10.00 – 5.00) / 29 + (13.93 – 10.00) / 17 = 0.564880586 hours
0.564880586 hours = 0.564880586 * 60 minutes = 33.8928352 minutes
0.8928352 minutes = 0.8928352 * 60 seconds = 53.570112 seconds
Rounding up, ideal time at 13.93 = 00:33:54

Method II
Time = (5.00 – 0.00) / 31 + (10.00 – 5.00) / 29 + (13.93 – 10.00) / 17 = 0.564880586 hours
0.564880586 hours = 0.564880586 * 60 minutes = 33.8928352 minutes
0.8928352 minutes = 0.8928352 * 60 seconds = 53.570112 seconds
Truncating, ideal time at 13.93 = 00:33:53

Method III
13.93 is in the 3rd speed sector
Time to complete 1st speed sector = (5.00 – 0.00) / 31 = 0.161290323 hours
0.161290323 hours = 0.161290323 * 60 minutes = 9.67741938 minutes
0.67741938 minutes = 0.67741938 * 60 seconds = 40.6451628 seconds
Truncating, ideal time at end of 1st speed sector = 00:09:40

Time to complete 2nd speed sector = 00:09:40 + (10.00 – 5.00) / 29 = 00:09:40 + 0.172413793 hours
0.172413793 hours = 0.172413793 * 60 minutes = 10.34482769 minutes
0.34482769 minutes = 0.34482769 * 60 seconds = 20.6896614 seconds
Truncating, ideal time at end of 2nd speed sector = 00:09:40 + 00:10:20 = 00:20:00

Time at 13.93 = 00:20:00 + (13.93 – 10.00) / 17 = 00:20:00 + 0.231176471 hours
0.231176471 hours = 0.231176471 * 60 minutes = 13.8705883 minutes
0.8705883 minutes = 0.8705883 * 60 seconds = 52.235298 seconds
Truncating, ideal time at 13.93 = 00:20:00 + 00:13:52 = 00:33:52

Method IV
13.93 is in the 3rd speed sector
Time to complete 1st speed sector = (5.00 – 0.00) / 31 = 0.161290323 hours
0.161290323 hours = 0.161290323 * 60 minutes = 9.67741938 minutes
0.67741938 minutes = 0.67741938 * 60 seconds = 40.6451628 seconds
Rounding up, ideal time at end of 1st speed sector = 00:09:41

Time to complete 2nd speed sector = 00:09:41 + (10.00 – 5.00) / 29 = 00:09:41 + 0.172413793 hours
0.172413793 hours = 0.172413793 * 60 minutes = 10.34482769 minutes
0.34482769 minutes = 0.34482769 * 60 seconds = 20.6896614 seconds
Rounding up, ideal time at end of 2nd speed sector = 00:09:41 + 00:10:21 = 00:20:02

Time at 13.93 = 00:20:02 + (13.93 – 10.00) / 17 = 00:20:02 + 0.231176471 hours
0.231176471 hours = 0.231176471 * 60 minutes = 13.8705883 minutes
0.8705883 minutes = 0.8705883 * 60 seconds = 52.235298 seconds
Rounding up, ideal time at 13.93 = 00:20:02 + 00:13:52 = 00:33:54

To summarize:

Method I Method II Method III Method IV
4.32 00:08:22 00:08:21 00:08:21 00:08:22
9.05 00:18:03 00:18:03 00:18:02 00:18:04
13.93 00:33:54 00:33:53 00:33:52 00:33:54

So how do you get around this?

Before the rally, talk to the organizer and figure out how they are calculating ideal times. If it is one of the 4 ways described above, go to “Results Type” in your TSDMeter Settings screen and choose “Computer” (Method I), “PB” (Method II), “Calcutta” (Method III) or “HMA” (Method IV). If not, let us know!

### 2 Responses to Quirks in ideal time calculations

1. Sudev Barar

Interesting. And leads to lots of problems.

Best method would be to continue accumulating fractions till you hit a TC. Here the fractions can be discarded as you now have a fresh start time based on in time out or some add up rule.

The reason being the distance and speed zones are part slices of the whole and not by themselves signifying anything. The significant distance is from one TC to the next and all zones in between apply.