Haunted Haul Footrace Course Details

The Haunted Haul Footrace was measured in accordance to USATF Course Measurement Standards

Course distance will be measured in accordance with USA Track and Field road race guidelines available from <http://www.usatf.org/Products-/-Services/Course-Certifications/USATF-Certified-Courses/Procedures-Manual.aspx> . The only exceptions to these guidelines will be:

1.  I will give priority to accuracy rather than to assuring a “not too short”course. Therefore the 1.001 (not too short factor) will not be used. However, the shortest actual course measurement will be used as it should indicate the shortest possible running path on the trail. Also the shorter of the calibration data sets will be used.

2. Bicycle wheel revolutions will be counted with a Vetta Cycle computer rather than a mechanical Jones Counter.

USING THE VETTA CYCLE COMPUTER:

The Vetta cycle computer will be set to a 2.5 “meter” wheel circumference so that 40 revolutions is exactly 100 “meters ” ( 0.1 “km”).  The quotations indicate that these are not real meters and km unless the tire circumference were 2.5 meters exactly which it is not. You would think that a 2.500 meter circumference input would mean that every 0.1 “km” increment shown on the Vetta Computer readout would indicate another 40 revolutions traveled. However, the business side of Vetta must have stepped in to lower costs. Thus Vetta uses a base 30 number system to report revolutions traveled. The first 0.1 “km” readout occurs after 60 counts (not 40) , the 0.2 “km” readout indicates an additional 30 counts (for 90 total counts not 80) sensed, but  0.3 “km” indicates another 30 counts sensed to yield the 120 counts which indicate that exactly 300 meters have been travalled . This pattern then repeats: 60,30,30,60,30,30,…so each 0.3 “km”  is right on at 120 counts. I verified this pattern by moving the wheel magnet back and forth over the sensor.

Below are 3 different patterns for different tire circumference inputs. Note that Integer values of wheel rotation result in very predictable patterns. The  2.500 meter circumference setting:  40 count/100 meter  (actually 120 count/300meter pattern) allows for the fewest revolutions between readouts of the integer divisions of 100 meters available to this computer.

 

2.000 pattern (50.00 counts per 100 meters) :60,60,30,60,60,30,60,60,30,60,60,30,60,60,30,60,60,30,60,60,30,… easy to predict, precise every 0.3 “km” ( but 150 counts between repetitive intervals)

2.096 pattern (47.71 counts per 100 meters) :60,60,30,60,30,60,60,30,60,30,60,60,30,60,30,60,60,30,60,30,60,…. Still gives closest approximation in increments of 30 counts but not as predictable a pattern, although so far it repeats every 5 counts eventually it should depart from this to distinguish from a slightly different circumference input (unless accountants are Gods at Vetta)

2.500 pattern (40.00 counts per 100 meters) :60,30,30,60,30,30,60,30,30,60,30,30,60,30,30,60,30,30,60,30,30,…. easy to predict, precise every 0.3 “km” with only 120 counts between repeating intervals

That the patterns are repeatable over a 6 mile distance was validated by the error between two 6 mile rides around a high school track. I attempted to stay 30 cm from the edge of the track to obtain 400 meters per lap. With the Vetta set to 2.096 meter circumference, my distances between trials were off by about 1.25 rotations off or about 2.6 meters  after 6 miles ( 24 laps and 56.064 meters). This total length error would result from a mere 3 cm error in judging lap radius.

For the 2.5 “meter” circumference setting the Vetta reports the exact 120 counts every 0.3 km the off counts are predictably less. Therefore we can ride the bike to within 30 to 60 revolutions of our desired race distance and then dismount and walk forward, counting the remaining revolutions to reach our goal distance. Fractions of a wheel revolution can be obtained by counting the 32 spokes. Thus the Vetta computer can be used as a tire rotation counter. One note of caution, the way I have the computer magnet mounted the first count is not a rotation. The tire rotates about one spoke before sensor registers  the first count. The first full rotation and a spoke is indicated by the second count. Thus one must add almost a full wheel rotation to achieve a required distance. For instance when the Vetta reports 0.1km, the Vetta has counted 60 sensor magnet passes but only 59  revolutions have occurred when the start mark on the wheel hits the ground. This is important because 1 revolution is about 2.1 meters which is about the size of our largest errors. I have the magnet before the first revolution rather than after so that I will not roll past the distance I want to mark.

CALIBRATION COURSE (TO BE USED ON ALL COURSE MEASUREMENTS):

Distance per tire revolution will be calibrated on a roughly 382 meter (actually it came out to be 377 meters)  section of straight roadway with a steel tape. This distance is  about a quarter of a wheel rotation past where the Vetta readout changes from 0.3 to 0.4 km. (Note that the Vetta will change to this value after 180 counts and 179 wheel rotations since I have the magnet positioned to read at the start of the first rotaion.)

The Bike Calibration course was in Mount Shasta City California on a recently resurfaced section of N. Old Stage Road on the side of the street opposite the Hummingbird Way loop. This section has a freshly painted straight white side line on which to tape and ride a bike in a straight line.  This calibration course is a refreshing 6 mile ride from Lake Siskiyou.

RESULTS: 2012 Oct. 20 Calibration course measurement (Done between 12:42 and 1:12 PM):

A 100 foot steel tape was used to measure between 2 drilled  1/8 inch diameter  holes into the asphalt. I filled these with epoxy, to avoid road decay.The two holes were made so that the front tire of my bicycle would roll 180 and a quarter rotations and just change from 0.3 to 0.4 “km” ( remember I have the tire circumference falsely set to 2.5 meters when it is closer to 2.1 meters, so I can used the “km” readout as a revolution  counter with 120 revolution for every 0.3 “km” readout ).

Start temperature = 67.5 degrees F,

Steel Tape always pulled to 10 pounds force with a fish scale. Masking Tape was placed on the ground and marked with a ball point pen to indicate the end of each 100 foot section.

Measurement 1: 12 lengths of 100 foot tape plus 39 feet 7  and 5/8 inches

Measurement 2: 12 lengths of 100 foot tape plus 39 feet 8 and 3/8 inches

Average of these 2 length measurements = 1239 feet plus 8 and 0/8 inches = 1239.67  +/- 0.05

Finish Temperature = 63.5 F

Average Temperature = 65.5 F.

Steel Tape Temperature Correction factor = [( Average Temp in Fahrenheit - 68.0 ) x 0.00000645 ] + 1  = 0.999983875 = [( 65.5 - 68.0 ) x 0.00000645 ] + 1  = 0.999983875

(formula taken from USATF certification procedures)

Temperature Compensated Calibration Course Length = Average Length of Calibration course, Multiplied by steel tape temperature correction factor = 1239.65 +/- 0.05 feet  (377.845 +/- 0.015 meters)

So our actual tire circumference is about roughly 377.845 meters / 179.25 rev = 2.108 meters. This is close to the 2.120 meter value I had counting 47 revolutions rolling 99.66 meters measured with a cloth metric tape measure. And close to the 2.096 meter value I had from riding around a high school track

This Length will be used to determine counts per distance before and after riding the race course.

ORIGINAL AROUND THE LAKE COURSE MEASUREMENT (Course not used due to aluminum scaffold bridge removal in delta)

Results: 10/21/2012 BIKE CALIBRATION BEFORE COURSE MEASUREMENT (How many tire revolutions to ride the 1239.65 foot Calibration course)

Initial tire pressure, 60 +/- 0.2 psig front and back tires (taken about 20 minutes before the calibration course was run.

Bike warmed up for 6 minutes before calibration test.

Time of Calibration Rides: 11:12 to 11:33

Temperature during Calibration Rides: 49.5 rising to 52 F

Rotations to do the Calibration Course ( at least 4 times back and forth)

179 revolutions and 11.7  spokes (uphill) (a spoke is 1/32 of a revolution)

179 and 9.2 spokes (downhill)

179 and 12.6 spokes (downhill)

179 and 7.2 spokes (uphill)

179 and 10.7 spokes (downhill)

179 and 8.4 spokes (uphill)

(Strange you would think I would ride straighter downhill)

Average rotations to do the calibration Course 179 and 9.96666667/32 rotations)

Sample Standard Deviation of these measures: 2.05 spokes.

dividing by the square root of 6 we get the standard deviation of the mean and our expected error = 2.05/ sqrt 6 = 0.83 spokes = 0.026 revolutions. Multiplying this systematic error over the length of the course means multiplying by 4 (quarters of a mile) x 6 miles = 24 times bigger error .     0.026 x 24 = 0.62 revolutions error.   So multiplied by our 83.0 inch wheel circumference this is a 52 inch error. This turns out to be our largest error. In the future I many want more calibration rides to reduce this error

Rotations per mile (= Ave rotations / (1239.65 calibration distance in  feet) x  (5280 feet/mile) =

179.3114583/1239.65 rev x 5280 ft/mile = 763.7353285 rev/mile = 6 feet and 10 and 15.37/16  inches / rotation = 2.1072 meters / revolution

Note that we have to add a count to the counts to get any distance because of the first freebee count at the start of the ride.

What this translates to on the Vetta Cycle computer is found by dividing by 120 rev per 0.3 “km”, subtracting out the whole number to leave the decimal. multiplying the remaining fraction by 120 to get back the revolutions past the 0.3 “km increment. If 60 or greater revolutions subtracting out 60 revolutions to get another 0.1 “km. If the remaining revolutions are 30 or more, subtracting out another 30 revolutions for another 0.1 “km” reading. Then subtract out the remaining full revolutions. Multiply the remainder by 32 to get the number of spokes beyond these revolutions. Multiply the 0.3 km segments by 3 to get the “km” count. Add one to the revolutions to get the actual Vetta count (one more than revolutions) then add in the additional “km” from the revolution over 60 and 30.

For Example: 1 mile will read out after 763.7353285 tire rotations. (we will add in the additional start count later otherwise when we multiply this mile number for different mileages we will be off)

So 763.7353285 / 0.3 “km” = 6.139461071 intervals of 120

= 6 x 0.3 “km”   +    0.139461071  (0.3 “km” intervals)

=1.8 “km”    +   0.139461071  x 120 rev/0.3″km”

= 1.8 “km”   + 16.7354052 rev

= 1.8 “km”   + 16 rev    +    0..7354052 rev (multiply this last fraction of a revolution by 32 spokes)

= 1.8 “km”   + 16 rev    +    23,53 spokes

Now we add one more revolution for the start count to get

=1.8 “km”   +  17 COUNTS + 23.53 spokes   (1 mile Vetta readout and revolution count)

FOR THE TOTAL 6 mile DISTANCE

763.7353285 rev/mile x 6 miles = 4582.411971 rev

= 38.18676643 (0.3 “km” increments

=  (38 x 0.3 “km” increments) + 22.411971 rev

= 11,4 “km” + 22 rev + 13.18 spokes

= 11.4 “km” + 23 COUNTS + 13.18 spokes          (6 mile Vetta Readout and visual revolution count)

IT IS INSTRUCTIVE TO LOOK AT THE 5 MILE CALCULATION TO SEE WHAT IS DONE WITH A LARGE REVOLUTION REMAINDER:

5 miles x 763.7353285 rev / mile = 3818.676643 rev

=31.82230535 (0.3 “km” increments of 120 rev.)

= (31 x 0.3 km) + (0.82230535 x 120)

= 9.3 km + 98,67664249 rev

the pattern of revolutions counts after 0.3 km increments is 60, 30,30 so the next 0.1 km is a 60 count and the one after that is a 30 count so

= 9.3 “km” + 0.1 “km” (60 rev) + 0.1 “km” (30 rev) + 8.67664249 rev

= 9.5 “km” + 8 rev + 21.65 spokes

Add in the starting free bee count to get
= 9.5 “km” + 9 COUNTS + 21.65 spokes  (5 mile Vetta Readout and revolution count)

Course measurement ride:

I rode the course once backwards and marked the start line with a steel spike driven into the ground. Then I rode the course forwards and the finish line was 34 inches past where I originally had it. So I rode to the start again and moved the start 34 inches back.  This discrepancy is most likely the result of riding a slightly tighter line the return trip. USATF will accept a discrepancy here of 0.08% which is 25.3 feet for a 6 mile course so at under 3 feet we are well within USATF standards for a road race.

First Course ride: 1:00 pm -2:24 PM , 55 F rising to 59 F

Second Course ride 2:48pm – 3:38 pm. 59 F rising to 62 F

Note that these temperatures are higher than the calibration temperatures so the tires should expand and I should error on the side of a longer course.

Results: 10/21/2012 POST COURSE MEASUREMENT BIKE CALIBRATION on the 1236.65 foot course

Time of Day 4:51-5:07

Revolutions to ride the 1239.65 foot calibration course:

179 + 10.5 spokes (downhill)

179 + 6.6 spokes (uphill)

179 + 10.4 spokes (downhill)

179 + 6.9 spokes (uphill)

(Again get the strange smaller count going uphill. )

Average rotations to do the calibration Course 179 and 8.6 /32 rotations (Note there are 32 evenly spaced spokes so each spoke is 1/32 of a revolution)

Ave cal. course rotations = 179.26875   (Since it is hotter during this calibration we would expect the tires to expand and yield the lower average revolution count)

dividing this count by 1239.65 feet cal course length and 5280 ft/mile yields 763.5534223 rev/mile. Over a 6 mile course this is 4581.320534 rev.

This value of revolutions is 1.09143698 revolutions less than the pre-course ride calibration so using this data would result in a shorter course by 1.09143698 x 83 inches = 91 inches

Sample Standard Deviation of the calibration revolutions is: 2.14 spokes.

dividing by the square root of 4 trials we get the standard deviation of the mean and our expected error = 2.14/ sqrt 4 = 1.07 spokes = 0.033 revolutions. Multiplying this systematic error over the length of the course means multiplying by 4 (quarters of a mile) x 6 miles = 24 times bigger error .     0.033 x 24 = 0.80 revolutions error.   So multiplied by our 83.0 inch wheel circumference this is 66 inches.  This error is overwhelmed by the 87 inch under measurement of the course that would be incorporated if we averaged in the second calibration distance. Therefore we will error on the side of a longer course and not use this second calibration course data.

Temperature = 55 F at end of second calibration course ride.

Final tire pressure = 61 psig  +/-  0.2 psig front and  60 psig back tire.

ORIGINAL COURSE MEASUREMENT FINAL RESULT : 6 miles maybe as much as 16 feet too long, and maybe as much as 5.4 feet too short. Also there could be a asphalt calibration vs dirt course factor.(see below this is a big factor)

COURSE MEASUREMENT ERRORS ( VALUES SHOWN ARE THE OVERALL EFFECT ON THE ENTIRE 6 MILE COURSE):

Calibration  course layout (3/4 inch difference in 2 measurements implies: +/-   18 inches

Bike Calibration Error: (Standard deviation  6 rides of the mean rotations to run the calibration course) +/- 52 inches

Not factoring in post course Bike Calibration + 87 inches after 4 rides

Course run first time was shorter by 34 inches, I took the longer value but perhaps I could find and even tighter line so: +/- 34 inches

Temperature Compensation the Temperature was hotter during the course measurement relative to the calibration rides.

The average temps Calibration ride 1 = 50.75 F, ave revolutions =  179 + 10 spokes

Calibration Ride 2 Temp = 55 F , average revolutions = 179 + 8.6 spokes

Course Ride Average 58.75 F

Assuming ideal gas behavior proportional to  temperature and linear tire expansion we have – 1.4 spokes / 4.25 F = – 0.33 spokes per degree F.  revolution adjustment.. So for the course measurement we used the calibration from the first calibration ride so that was done at a temperature of 8  F less. so 0.33 spokes/F * 8 F = should have = -  2.64 spokes. over the calibration course  = 0.0825  revolutions  over the  calibration  course. or 4 x that  per mile and 6x that for 6 miles makes 1.98 rev  over 6 miles. and with a 83 inch revolution this is results in a  164 inch longer course. I could get rid of this factor by calibrating at temperatures both higher and lower than the ride temperature.

Known errors which would result in a longer than 6 mile course are:  18 +52 + 87 + 34 + 164  = 355 inches (30 feet)  too long a course

or -18-52-34  = -104 inches = 9.7 feet  shorter than 6 mile course

The above errors are exaggerated since the probability of all errors being in the same direction is low.

These errors should not add directly together since they are independent we should actually be adding them in a root of sum of squares manner:

TOO LONG ERRORS : ROOT OF SUM OF SQUARES: SQRT(18^2 +52^2 + 87^2 + 34^2 + 164^2) = 197 inches  = 16 feet

TOO SHORT ERRORS : ROOT OF SUM OF SQUARES: SQRT(18^2 + 52^2 + 34^2) = 65″ = 5.4 feet

But all this is moot because flood control just called and the bridges are to be removed Thursday therefore we have to measure the Alternate course..

Unknown factors: Course is mostly dirt and some gravel and asphalt. While the calibration course is asphalt.

SURFACE CORRECTION FACTOR FOR DIRT:

I compared Riding on asphalt and dirt on a section of straight road just north of Box Canyon Dam on 10/23/2012 with the  surprising result that the front tire under-estimates mileage on dirt compared to asphalt. (The front tire may skid a bit on the trail and therefore not turn as much)

Raw data in order of data taken:

Asphalt going uphill: 5 “km” + 3 revolutions + 21.5 spokes = 213.67 revolutions

Asphalt going downhill: 5 “km” + 3 revolutions + 24.7 spokes = 213.77 revolutions

Dirt going up: 5 “km” + 3 revolutions + 3.0 spokes = 213.09 revolutions

Dirt going down: 5 “km” + 3 revolutions + 13.3 spokes = 213.04 revolutions

Asphalt going up: 5 “km” + 3 revolutions + 26.9 spokes = 213.84 revolutions

Asphalt going down: 5 “km” + 3 revolutions + 25.9 spokes = 213.81 revolutions

Dirt going up: 5 “km” + 2 revolutions + 31.7 spokes = 212.99 revolutions

Dirt going down: 5 “km” + 3 revolutions + 14.2 spokes = 213.44 revolutions

Comparing the data in a more organized form:

Asphalt up__:213.67,  213.84_______Dirt up__:  213.09, 212.99

Asphalt down:213.77 ,213.81_______Dirt down:  213.04, 213.44

Asphalt tends to read more revolutions than Dirt (shorter length/rev). Therefore I have an error on long side when measuring on dirt after calibrating on asphalt

Asphalt average +/- sample standard deviation of mean = 213.77 +/- 0.04

Dirt average +/- sample standard deviation of mean = 213.14 +/- 0.10 (fewer revolutions for the same distance means will measure course longer by a factor of 213.77/213.14 = 1.0029)

Dirt correction factor 0.3% +/- 0.03 % . This is huge compared to the combined error I calculated above. This means I have a built in short course prevention factor of 0.3 % rather than the USATF suggested 0.1 %

This means our 6 mile course can be expected to be 95 feet too long (NOT QUITE THIS LONG BECAUSE IT IS NOT ALL DIRT) So I should correct for this for the dirt portions of the course. Recall the combined total of the other errors over 6 miles was 16 feet too long to 5.4 feet too short. The surface correction factor is important! also there is uncertainty to this correction factor because the surface varies from hard packed to rocky to sandy.

 

THE ALTERNATE (DELTA OVERFLOW) COURSE

The full alternate Course measurement was done today (10/25/2012) was quite challenging with interweaving paths along the route to the beach. Measuring the main trail was much easier. I can see why USA=Track and Field likes the Jones counter. No counting those 30 to 60 wheel revolutions between tenth kilometers allows you to watch the path and not wander off into the bushes.

BIKE CALIBRATION BEFORE ALTERNATE COURSE MEASUREMENT (I did 5 rides back and 5 forth to increase calibration ride accuracy)

Bike tire pressure:  60 psig both front and back.    Warm up time:   65 minutes : Temperature Range: 43.5 to 43.0  Time Range:11:03-11:34 am,

Order of measurements up down up down….(north,south, north, south)

179 revolutions + the following spokes: 5.0, 9.95, 5.5, 7.4, 4.6, 11.4, 5.7, 9.8, 5.95, 11.2

average of spoke counts = 7.65 +/- 2.67/(sqrt 10) = 7.65 +/- 0.84

so the total rev/mile is ( 179 + 7.65/32)rev / 1239.65 x5280 ft/mile = 763.42675 rev/mile or about 2.1081 meters/rev = 82.99 inches as previously. used on the Original course.

 

BIKE CALIBRATION AFTER ALTERNATE COURSE MEASUREMENT (again a total of 10 rides back and forth was done)

Warm up tires: 5:41-5:46, Initial Temp = 45.5 F

Measurements taken in up down up down…… pattern  also known as  North South North South…)

All measurements are all 179 tire revolutions plus the number of spokes listed (1/32 of a revolution)

Up: 4.9, 6.3, 8.15, 5.75, 6.5 (The 4.9 measurement I came in a bit fast and had to break hard so this measure could be fewer rotations than real)

Down: 14.3, 10.8, 12.6, 12.6, 11.4  (The 14.3 measurement I was playing chicken with a car trying to stay firmly on the white side line but I gave in and I moved out of the way so I went a longer route with more rotations)

In order the numbers were 4.9, 14.3, 6.3, 10.8, 8.15, 12.6, 5.75, 12.6, 6.5, 11.4

Average +/- Sample Standard Deviation of the Mean.  = 9.33 +/- 3.92/ SQRT (10) = 9.3 +/- 1.2

Eliminating the first 2 dubious measures  yields:  9.26 +/-  2.9/sqrt (8) =  9.3 +/- 1.0  So either way I have essentially the same result.

This yields a revolutions per mile of (179 + 9.3/32 ) / 1239.65 ft calibration course x 5280 ft/mile = 763.6464 rev/mile means 2.1074 meters/rev . This lesser length/rev would result in a longer course

end Cal time = 6:19 pm, end Cal Temp: 41.5 deg (was 45.5 at start of this cal. at 5:46, sun went down)

Ending Bike pressure at home: 6:26pm Front 59.5 psig, back: 60.5 psig

COURSE LENGTH MEASUREMENT

Backwards  strt at 3:06 to 4:05 at 47 F to 47 F

Forwasds strat at 4:12 to 5: 16 at 47 start to 45 F end temp

11.3 + 8 rev + 3.3 spokes

= 37 2/3 (0.3 “km”) + 8rev +3.3 spokes

= 11.1 “km” +60 rev + 30 rev + 8 rev +3.3 /32 rev =

= 120 rev x 37 + 90 rev + 8 rev +3.3/32 =

=4538.103125 rev / 763.42675 rev/mile = 5.9443858 miles  (GPS read 5.95 before subtracting for walk of 23.5 x 2 foot steps x3 = 0.02 miles during overshoot so 5.93 miles corrected GPS matches within 0.01 mile)

Second run in forward direction

7.5 + 8 +20.7 spokes (plus 2 miles since I re-zeroed at 2 miles after inadvertently moving the bike forward)

= 2 miles (3.7 rev + 26 rev + 27.31 spokes  then re-zeroed ) then at finish reading 7.5 “km” + 8 rev + 20.7 spokes

7.5 “km” + 8 rev + 20.7 spokes=

= 7.5/0.3 km + 8 rev + 20.7/32 =

= 25 x 120 rev/0.3km + 8.646875 =

= 3008.646875

= 3008.646875  x / 763.42675 rev/mile =3.9409765 miles

So the total miles for the second measurement of the course comes out to be 5.9409765 miles which matches my GPS reading of 5.94 miles to within the GPS readout precision.

The first measure yields the longer course but I overshot on this measurement on one turn.  the discrepancy of 0.003409291 miles = 18.00 feet = 216.01 inches could easily be accounted for by my pace inaccruacy.

Other errors in the measurement are:

Calibration course inaccuracy of 18 inches

Calibration bike course inaccuracy of 0.84 spokes = 0.026 rev per the 1239.65 foot course . So over 6 miles this is 0.026 rev/cal course x 83 inches/rev x 1 cal course / 1239.65 ft x 5280 ft/mile x 6 miles = 56 inches

COURSE MEASUREMENT ERRORS ( VALUES SHOWN ARE THE OVERALL EFFECT ON THE ENTIRE 6 MILE COURSE):

Calibration  course layout (3/4 inch difference in 2 measurements implies) 0.75 inch / 1239.65 ft cal course x 5280 ft mile x 5.94 miles = : +/-   19 inches

Bike Calibration Error: (Standard deviation  6 rides of the mean rotations to run the calibration course = +/- 52 inches

Course run first time was shorter by 18 feet  inches,  but I really messed up this measure.

Temperature Compensation the Temperature was hotter during the course measurement relative to the calibration rides.

The average temps Original course Calibration ride 1 = 50.75 F, ave revolutions =  179 + 10 spokes

Calibration Ride 2  on Original course Temp = 55 F , average revolutions = 179 + 8.6 spokes

Course Ride Average on original course: 58.75 F

Assuming ideal gas behavior proportional to  temperature and linear tire expansion we have – 1.4 spokes / 4.25 F = – 0.33 spokes per degree F.  revolution adjustment.. So for the course measurement we used the calibration from the first calibration ride so that was done at a temperature of 8  F less. so 0.33 spokes/F * 8 F = should have = -  2.64 spokes. over the calibration course  = 0.0825  revolutions  over the  calibration  course. or 4 x that  per mile and 6x that for 6 miles makes 1.98 rev  over 6 miles. and with a 83 inch revolution this is results in a  164 inch longer course.

Doing these same calcs on the Alternate course data ……. ( have not done this yet)

These errors should not add directly together since they are independent we should actually be adding them in a root of sum of squares manner:

TOO LONG ERRORS : ROOT OF SUM OF SQUARES: SQRT(19^2 +a^2 +b ^2 +  c^2 + d2) = xinches  = x feet

TOO SHORT ERRORS : ROOT OF SUM OF SQUARES: SQRT(19^2 + x^2 + y^2) = x” = x feet

SURFACE CORRECTION FACTOR FOR DIRT relative to Asphalt: 0.3% (see data above). Asphalt covers from GPS mile 1.76 to 2.29 and 2.71 to 2.82 mile readings meaning 0.53 mile  + 0.11 mile = 0.64 mile or  10.8 % of the course so the correction factor is 0.892 x 0.003 = 0.0027

ALTERNATE COURSE LENGTH MEASUREMENT FINAL RESULT About 5.94 miles for the whole course by GPS. with the surface correction factor the bike wheel turn measurement would actually read a shorter course because we have a reading of 5.944  (1st run ) 5.940 miles  second run.

If we take add in the +0.2.7% dirt correction factor  = these are:  and 5.944 x 1.0027 = 5.960 miles (1st course measurement ride) and 5.941 x 1.0027 = 5.957 (second course measurement ride). These are longer so by USATF standards we should use the shorter GPS length of 5.94 miles which means the current course is 317 feet short. I  extended the 180 degree turn around point which is .2 mile from the finish by 1/2 this distance to adjust the finish line to  6 miles or longer. A second GPS measurment bike ride a 7 am the morning of the race extended the finish another 2 yards longer. QED (Geeks know QED is a initialism of the Latin phrase quod erat demonstrandum, originating from the Greek analogous hóper ódei deîxai (ὅπερ ἔδει δεῖξαι), meaning “which had to be demonstrated.” QED explanation from Wikipedia )

Actually I have not shown much here. My bike wheel measurements seemed to be right on with the GPS measurements until I included the the dirt correction factor of a whooping 0.3% to give a shorter course measurement than the GPS reading. To do the wheel measurements more accurately I would have find out why the section of road where I compared dirt to asphalt and  obtained the dirt correction factor from differed from my actual course. I probably need to have various correction factors for different sections of trail. Of course, most trails do not  have 300 meter straight sections necessary for a proper steel tape measured calibration segment. Conclusion: GPS is the way to go for off road races USATF guidelines are accurate only when the calibration surface matches the course surface .