Straightness

I have start places and finish places of each Grand Tour stage in my database, and also the length. As a sanity check, I calculated the straight line distance between start and finish. The real length of a stage should be as least as long, so this is a method to find mistakes.

Below are lists of the 25 stages per Grand Tour where the ratio real length/straight length is the largest.

There are a few sources for errors:

• De distances were not always indicated very accurately. Nowadays, this is done using GPS, but a century ago, the distance between start and finish was given less accurately. The error will be in the order of a few kilometers.
• The coordinates of start and finish are not exact. I used the coordinates that I found in Wikipedia when I searched for the relevant location. This can also be off by a few kilometers. Moreover, the coordinates refer to the center of the city, which is not necessarily the place where the start or finish were held.
• To calculate the straight distance, I use the haversine equation. This assumes that the earth is a perfect sphere, what is not true. The error that this creates is smaller than a kilometer.

Altogether, this makes an worst case error of a few kilometers (assuming that the error sources above are independent), and because a typical stage has a length of 200 km, a ratio of 1.02 can still be correct. Every stage that has a ratio above 1.02 needs an explanation or improvement.

For the Tour, there are only two anomalies:

• 1988 prelude: the length of the stage is given as 1 km, but this started with a team time trial of 5 km. It was a ridiculous format, which I can not really fit into my system.
• 1976, stage 18A: this stage was shortened from 133 km to 86 km, but the start was still given at the original location, after which riders were transported by cars. This was because the riders were too tired from the previous day.

All other stages (should) have a ratio below 1; a value slightly above 1 could indicate a rounding error.

I also did this for the Giro, see below. Exception is:

• 1946, stage 5A: over a straight line between Bologna and Cesena (following the SS9), with start and finish outside the city centers.

And for the Vuelta. Exceptions:

• 1956, stage 3: First 80 km were neutralized because of heavy snowfall.
• 1957, stage 12: Started in Barcelona, but the first part was neutralized, and the real start was around 70 km West of Barcelona (in Igualada).
• 1958, stage 4: Started in Zaragoza, but the first part was neutralized, and the real start was around 70 km West of Zaragolza (in Hostal Ciervo, Los Monegros).
• 1961, stage 9: Started in Albacete, but the first part was neutralized, and the real start was around 55 km West of Albacete (in Minaya).
• 1995, stage 4: First 73 km were neutralized because of hard winds, real start was in Villalba.

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