Calculating the Opening and Closing Times of Controls

Below the line is a deeper explaination of the math behind the openning and closing times. Most organizers go straight to the Rusa calculator at rusa.org:

To confuse matters I have 2 sources with 2 formulas for calculating the limits. The first one has been on this site for years - I believe it's from the English language Randonneur Mondeaux site ~ 2000 put together a little earlier by Johnny Bertrand (USA). The second is from the ACP web site in 2010. This part of "article 10" is only in the French version of the rules. Presumably the ACP formula is the correct one, but I'm not sure so I'm leaving the other one here.

Time Limits Formula #1:

The formula for calculating opening and closing times is based on a series of average times which shift as an event proceeds. Here are the values:

EXAMPLE: Let's suppose you want to have a control at 442 km in a brevet with a 6 a.m. start time. The 442 km control opening time would be at 6:32 p.m. on day 1, and the closing time would be at 11:28 a.m. on day 2. Here's how we get these figures:

The opening time can be found by adding the first 200 km portion [34 km/hour is 200/34 = 5.88 hours (~5:53)], to the second 200 km [32 km/hr is 200/32 = 6.25 (6:15)], and then to the 42 remaining km [30 km/hr is 42/30 = 1.4 hours (1:24)]. 5:53 + 6:15 + 1:24 = 13:32 added to the 06:00 start time is 19:32 (or 7:32 p.m.). The closing time is easier: 442/15 = 29.47 hours (~29:28) added to the 06:00 start = 35:28 (or 11:28 a.m. on day 2).

Time Limits Formula #2 (from ACP web site 2010):

Article 10 : Les délais impartis pour effectuer chaque brevet sont fonction de la distance : 13h30 (200km), 20h (300km), 27h (400km), 40h (600km) et 75h (1000km).

Le passage dans chaque contrôle devra s'effectuer entre une heure "d'ouverture" et une heure "de fermeture" mentionnées sur la carte de route, calculées sur des moyennes extrêmes de 15 et 30 km/h pour les contrôles jusqu’au 600e km, de 13,5 à 30 km/h entre 600 et 1000 km.

Curiously, none of the sources I've found say anything about opening times calculations between 1000 and 1200 km.

Eric F