# Measurement of Calibration Course: The Mall

### Calibration by NIST of the tape used to measure the course

The tape was a 100m steel tape which had been calibrated by NIST. (See REPORT OF CALIBRATION, NIST Test No: 683/282295-12 April 24, 2012. Scans are available on David's website page1 page 2) The NIST test measurements showed:

At 10KgF tension and 20C, the true distance between the zero and 50 m marks on the tape was found to be 50.00661 m. This means that for every 50m tape length 6.6mm has to be added to the tape readings get the true distance.

The true distance at other tensions can be worked out from the following NIST test result from the distance between the 40m and 100m marks on the tape:

At 10KgF tension true distance = 60.00776 m; At 20KgF tension true distance = 60.02946 m

The standard tape tension pull specified by most tape manufacturers is 50N which is approximately 5.1 KgF (or 11lbF). Experienced measurers are able achieve sufficiently close to 50N by giving the tape a firm but not excessive pull.

One can calculate the true distance for 5.1 KgF tension from the 20KgF and 10KgF test results above:= 60.00776- (60.02946-60.00776)*4.9/10 = 59.9971m.

So the reducing the tension from 10KgF and 50N for 60m section of the tape is true distance is reduced by 10.66mm. This is a factor of 59.9971/60.00776 = 0.999822

Applying this factor to the 0 to 50m true distance of 50.00661 m we get a true length at 50N tension of 49.9977 m, so at 50N the tape markings are very nearly exact, we have to subtract just 2.3mm for each 50m tape length (at 20C).

### Correction for temperature of 11C experienced during the taping of the Mall Course

NIST give an assumed temperature coefficient for a steel tape of 0.0000115 C-1.

At 11C correction to give the true distance for the 50m length is -50000*9* 0.0000115 = -5.2mm.

### Final corrected tape length for 50N and 11C

So at 50N and 11C the true distance from the 0 to 50m tape marks is 50m (-5.2 -2.3) mm = 50m – 7.5 mm = 49.9925 m.

### Details of calibration course and its measurement by the steel tape

A temporary calibration course was laid out next to the straight kerb on the South side of The Mall between the start/finish line and the Queen Victoria Memorial.

The endpoints used were in line with the East Faces of Lamp Posts No 18 and 30. Pieces of sticky tape were used on the road and these were marked to show the exact locations of the end points. The taped intervals were also marked in the same way.

David Katz and Hugh Jones carried out the course taping between 00:45 and 01:15 on 13 June 2012 immediately before calibrating the bikes and undertaking the measurement of the marathon course. The temperature was recorded as 11C.

One the first run with David marking the tape lengths and applying tension and Hugh holding the zero mark to the road marking, there were 6 x 50m tape lengths plus 28.645 m giving a total of 328.645 m before applying the corrections calculated above.

For the return measurement with roles reversed Hugh obtained a total length of 328.648 m

Average of two tapings= 328.6465 m. Correction is -7.5*328/50 mm = -49.2 mm

The Mall Calibration Course Corrected Length = 328.597 m

### Independent Check Using a Laser Ranger

Mike Sandford carried out a check on the calibration course length around 05:00 after the marathon measurement had been completed.

The laser was mounted 104 cm above the ground and aligned with the calibration course end marker by means of a plumb bob. The laser beam was aimed at retro-reflector placed on the ground. The reflection spot was approximately 10 cm above the ground.

A correction was deducted for the slope of the laser beam (worked out using Pythagoras) The plumb bob hung from a point 16mm behind the laser reference point. The course was measured in two steps, on the second step the plumb bob was aligned 12 mm SHORT of the calibration course marker position).

 Laser Readings (average of 3) Deduct extra arising from slope of laser beam Plumb line to laser ref point Refllection to front face Plumb to cal end mark After correction 159.539 -0.0029 +0.016 -0.0015 0 159.551 169.057 -0.0027 +0.016 -0.0015 0.012 169.081 Corrected laser total = 328.631

So the laser gave a measurement which was 328.631-328.597 = 34mm larger

As a percentage this is a difference of 0.010%

The specification for the laser, a Bosch Professional GLM 250VF, is as follows:

In unfavourable conditions (e.g. at intense sunlight or an insufficiently reflecting surface), the maximum deviation is ±20 mm per 150 m. In favourable conditions, a deviation influence of ±0.05 mm/m must be taken into account.

This spec is 0.013% in unfavourable conditions and 0.005% in favourable conditions.

Therefore, within the laser accuracy range stated by Bosch, the laser measurement confirms the measurement made with the calibrated tape .

The value of 328.597 m derived from the NIST calibrated steel tape measurements was taken as the calibration course length for the purpose of Olympic Marathon measurement.