Four Function Calculator Instruction Manual
By Fred Mapplebeck
This document describes a navigation scheme using a four function, ten digit calculator with memory, in conjunction with a watch reading to hundredths of a minute and having a split feature, and the car's stock odometer.
There are two levels of accuracy described. The first level uses mileage's measured to tenths of a mile (such as are available in many new cars using electronic odometers). This can also be used with rolling tenths, mechanical odometers by reading the odometer to the nearest tenth of a mile. This method is the easier of the two to implement (but a little less accurate).
The second level assumes that you are using a rolling tenths, mechanical odometer, and are reasonably proficient at estimating hundredths of a mile from the position of the tenths digit. It is usually best if the navigator is responsible for reading the odometer. In some cars this is relatively easy. In other cars, it can be quite difficult.
Three forms are used with this navigation scheme. The first is a speed/factor table which gets filled in at the end of the odometer check. (Editor's note: the first two forms are Word documents and downloadable from this site. The third form is an Excel spreadsheet also available.)
The second is a log. This has columns for various data such as instruction number, speed, time, etc. Both of these forms are used for either level of accuracy.
The third form is a set of tables of time and distance for various speeds for distances from 0.01 miles to 0.09 miles. These times are uncorrected for odometer correction factor, but the mileage's are so small that the errors are negligible.
II. Before you start
Before you start the rally, take a blank speed/factor table and highlight the speeds that are used in the rally. Synchronize your watch with official rally time. If you are using a stop watch, then you must start it on the hour. It is possible to use a watch that reads in seconds if you don't mind mentally converting the comparisons between the seconds on the watch and hundredths of a minute on the calculator, but it is a lot easier if you have a hundredths reading watch.
In some rallies, the rallymaster will give you mileages to some (or all) of the instructions. In those cases you can calculate the perfect time to arrive at an instruction before you start the rally using the following instructions (note: be careful not to go too fast as the calculator needs time for some calculations):
1. Push MEMORY CLEAR.
2. Enter the starting time in minutes and push M+.
3. Enter the mileage for the next instruction and subtract the mileage for the starting instruction.
4. Push the DIVIDE key and enter the speed.
5. Push the MULTIPLY key and enter 60.
6. Push the EQUALS key.
7. Push the M+ key.
8. Push the MEMORY RECALL key. The number is the time you should arrive at this instruction.
9. For pauses, enter the time in minutes and push the M+ key.
10. For pauses over a mileage, calculate to the mileage where the pause ends and write down the ending mileage.
11. To help avoid mistakes, circle the mileage for instructions where there is a pause over a mileage, and check off pauses as they are entered into the calculator.
IV. The Odometer Check
At the start of the odometer check, zero the odometer. You should take into account lag (if any) in your odometer. Lag is the mileage that it takes for the odometer to start rolling again after it has been zeroed.
At the end of the odometer check, note the mileage. Calculate an odometer correction factor from the equation: odometer correction factor equals measured mileage divided by official mileage.
For example, say that that your odometer reads 10.7 miles, and that the official mileage was 10.56 miles. The odometer correction factor is 10.7 / 10.56 = 1.01325. Write this in the space provided at the top of the speed/factor table. Store the correction factor in the calculator's memory. MC followed by M+.
Next calculate factors for the speeds that you have highlighted from the following formula: speed factor equals 6 divided by speed divided by odometer correction factor, plus 1000. Enter the result into the factor box beside the appropriate speed (only the first four decimal places are needed).
For example, using the odometer correction factor calculated above, the speed factor for 30mph would be calculated as follows - 6 / 30 / MR + 1000 = (where / is the calculator divide key). The result would be 1000.197383, and 1000.1974 would be written in the factor box next to 30mph.
If you have some extra time, you might want to calculate factors for some of the speeds that are not highlighted, in case the rallymaster uses one at a checkpoint. Start with the obvious ones, such as 30, 35, 40, etc.
V. Starting the Calculator
This section describes how to start the calculator at a given mileage, time and speed, such as might be done at the end of the odometer check, leaving a checkpoint, at the end of a transit zone, after calculating a time allowance, etc.
First put the speed factor in memory. For example, for 30mph, first push MC to clear the memory, then enter the speed factor for 30mph (1000.1973 in the example above) into the calculator and push M+. Next, enter the current mileage and multiply it by 10,000 and then add the time to it.
Suppose that in the example above you were supposed to leave the odometer check at 11:45.00. The keystrokes would be as follows - 10.7 X 10000 + 45.00 =. The resulting display would read 107045. (The next section will explain where the missing zeroes from the 45.00 went.)
VI. Reading the Calculator Display
The display contains both mileage and time. It is important to know how to separate the two. The key is the decimal point. The time is read as the two numbers to the left of the decimal point, and the numbers (if any) to the right of the decimal point. It is important to note that the calculator may display from none to four digits to the right of the decimal point. If it displays less than four, then you can mentally assume that there are zeroes following the number displayed.
In the example above, the number can be assumed to be 107045.0000, and the time being displayed would be read as 45.00 minutes. The mileage is the digits to the left of the minutes digits, with the decimal point assumed. Again, from the example, the digits to the left of the minutes digits is 1070. This should be assumed to have two decimal places, so the mileage is read as 10.70 miles.
A calculator display of 294027.385 would be read as 29.40 miles and 27.38 minutes. In this way we can accumulate both mileage and time at the same time in the calculator, thus simplifying our calculations and eliminating the need to keep track of the mileage separately.
Note that there is no provision for hours in the display. If you don't know what hour you are on, then the calculator will probably not be of much help.
You also might find it helpful to put a small mark on the calculator under the display that will indicate the mileage decimal point when the fourth time decimal point is non-zero. You can force this to happen at any time by adding 0.0001 to the display. This additional time is insignificant in computing your time error.
VII. Making Time Checks
Now that you have your calculator set to start, you need to make time checks as you rally. Assuming that you left the odometer check (or other starting point) on time, you can advance the calculator to some mileage that the car has not yet reached. This is done by pushing the + key followed by the MR key and then the = key. This will add 0.10 miles and the appropriate amount of time to the display. Additional amounts can then be added by just pushing the = key. Continue pushing the = key until you have the calculator mileage ahead of the car's mileage.
When the car's mileage reaches the mileage displayed in the calculator, push the split button on the watch. Compare the time on the watch with the time in the display. If the time on the watch is more, then you are late. If the time on the watch is less, then you are early. Mentally take the difference between the two numbers and let your driver know what the status is.
Continuing to use the example above, say that you pushed the = key three times and the display now reads 110045.5919. When the car's odometer reaches 11.00 miles, you push the split button on the watch and it reads 45.55. Mentally comparing this with 45.59, you inform the driver that s/he is 4 early.
After making a time check, you can then push the = key some number of times to get ready for the next time check. How often you do a time check is up to you. Pushing the = key will work as long as you remain at the same speed.
VIII. Speed Changes
When you get to a speed change, note the car's mileage, and enter it into the log. Increment (or decrement) the calculator until its mileage equals the car's mileage, and write the calculated time in the log. Now restart the calculator at the new speed, as described in section IV
For example, say that a speed change to 35mph occurred at 22.7 miles, and the calculated time was 52.84. Write these numbers on the log. Then clear the memory and enter the speed factor for 35mph from your speed factor table. Put this in memory by pushing the M+ button.
Then enter the mileage, multiply by 10,000 and add the time. So your display should look like 227052.84. (Note: after you have been doing this for a while you will probably be able to do the times 10000 in your head and enter the whole number (227052.84) at once.) You can then resume incrementing the calculator by pushing +, MR, and =. Subsequent pushes of the = key will add increments to the time and mileage.
At some point you will need to account for pauses (and gains). These can be handled quite easily. Just add (or subtract) the time, in minutes, to (or from) the displayed number.
For example, suppose that at 27.3 miles you execute an NRI that reads "STOP. Pause 15." Push the + key and enter .15 (pauses are sometimes given in hundredths of a minute, so you have to divide by 100 to get them into minutes) then push the = key.
To resume adding mileage and time as above, push +, MR, and then =. Then you can use the = key as before to continue adding increments of time and mileage.
At a checkpoint, you should note the mileage on the odometer, and increment the mileage on the calculator to that mileage. (Note: if the calculator mileage is already greater than the mileage at the checkpoint, you can decrement the calculator by pushing -, MR, and then =. Push the = key enough times so that the calculator mileage is the checkpoint mileage).
In your log note the mileage and calculated time to the checkpoint. It is usually a good idea to split your watch as you cross the line, and have the driver check this time against the time that the checkpoint crew got. When you leave the checkpoint, use section IV as a guide to getting the calculator started again.
XI. Transit Zones
Note the mileage at the beginning of a transit zone. Increment (or decrement, if necessary) the calculator until the mileage on the calculator is the same as the mileage at the beginning of the transit zone. Write down the mileage and time on your log.
When you get to the end of the transit zone, note the mileage again. Add the time allowed for completing the transit zone to the time you calculated at the beginning of the transit zone. Use this time, the mileage at the end of the transit zone, and the speed out of the transit zone to start the calculator again (as in section IV).
XII. The Log
One of the keys to any navigation scheme is to keep a log. On the sample log, there are boxes for entering NRI, Official Mileage, Actual Time of Day, Measured Mileage, Calculated Time, Pause/Gain, and Speed Change. As a minimum, you should fill in the NRI, Measured Mileage, and Calculated Time at each NRI and checkpoint. Except for official mileage, the remaining boxes can be filled in if you have time.
If your calculator has an automatic shut-off "feature", then at some point during the rally, you may not do anything to the calculator for a long enough period of time to cause it to shut off. When this happens, you will lose all your information.
This is not a problem as long as you have been keeping a log. Just turn the calculator back on and use section IV and the last line on the log to start up the calculator again. Then just increment the time and mileage to catch up to where the car's odometer is.
XIV. Advanced Calculations
The basic calculation method noted above will result in occasional errors due to the inaccuracy of measuring the mileage.
For example, let's say that you changed speed from 40 to 20 at a mileage of 21.5, but the mileage was really 21.45. The difference of .05 miles times the difference in speeds causes you to actually be about 0.07 minutes early when you think that you are on time. In general, these errors tend to cancel out, but occasionally they can accumulate.
In order to minimize the errors you need to be able to estimate your mileage readings to 0.01 miles. With a little practice, you can get reasonably proficient at this. This makes the procedure at speed changes a little more difficult, but the Speed Change Table will help to make it easier.
When you get to a speed change, note the car's mileage, this time estimating it to .xx miles. Increment (or decrement) the calculator until its mileage equals the car's mileage to the tenths digit and enter this info into the log. Clear the calculator memory and enter the speed factor for the new speed into the memory.
From the Speed Change Table enter into the calculator the number for the hundredths of a mile traveled at the old speed. Add the number for the hundredths of a mile traveled at the new speed, and then add the number read from the calculator at the mileage truncated to the tenth of a mile. When you have done all of this, write the new mileage and calculated time in the log.
For example, say that a speed change from 30mph to 35mph occurred at 22.74 miles, and incrementing the calculator to 22.7 miles gives a calculated time of 52.84, or 227052.8417. Write this down on your log.
On the next line of the log write the exact mileage of the speed change (to the hundredth of a mile). Clear the calculator memory and enter the speed factor for 35mph from your speed factor table into the memory.
From the speed change table, a distance of .04 miles at 30mph gives a number of 400.080. Enter this into the calculator. Add to this the number from the table for .06 miles at 35mph, or 600.103, giving 1000.183. Add to this the previous info, 227052.8417, giving 228053.0247, and write this on the log in the next line.
You can then resume incrementing the calculator by pushing +, MR, and =. Subsequent pushes of the = key will add increments to the time and mileage. Do this until it is ahead of the odometer and resume making time checks. This will improve your accuracy to the point where you have the potential of averaging about three points of error per leg (assuming no mistakes).
The table assumes that your odometer reads reasonably close to the rallymaster's odometer. If this is not the case, additional small errors can creep in. This can be (mostly) compensated for by redoing the table. Unless you are carrying around a lap top and printer, this can be pretty hard to do during a rally.
But you can make a reasonable estimate by comparing your odometer to statute miles (using a measured mile or the mileage markers along the interstates). The number in the upper left corner of the table is the odometer factor, as calculated in section III. You can calculate an odometer factor based on statute miles and adjust the table by setting the number in the upper left to the new factor. The times in the tables are divided by this number.