April 2001

The Curta and You

Curta Type I
Curta Type I

by David Hebb & Arthur Peck

taken from Sports Car Rallies, Trials, and Gymkhanas by David Hebb and Arthur Peck, Channel Press, 160 pages, hardbound & softbound, 1960 edition. Out of print. Slightly revised throughout, removes chapters on racing and regularity runs, and adds chapters on the Curta and speed tables from 15 to 39 mph.

Transcribed here is Chapter 10, pages 71-74.

At this point we step into a different world. Like Alice, in her memorable looking-glass break through, we find ourselves in a land where Things Are Different. The business of exact navigation to the second, hour after hour, imposes on us a discipline so strong that we sometimes wonder if we are in our right minds.

Distances are now calculated to within a hundredth of a mile less than 53 feet and the finesse of entering a checkpoint has been brought to such polish that skilled rally teams check in within a second time after time. Pity him whose watch is a second slow, or whose odometer is in error by a fraction of a tenth of a mile! Running a rally requires a high degree of concentration hour after hour, with little opportunity for enjoying the scenery. To some it is the most challenging of sports; to others it has all the thrill of filling out Form 1040.

The rally team that expects to make a good showing against earnest competition must realize that success is going to take a great deal of effort. As Harold S. Vanderbilt once said about yacht racing, "You don't win by going out sailing on Saturday afternoons." Successful rallying requires a successful technique, as nearly foolproof as possible, worked up to such a degree that the technique is virtually automatic. You will ask the conquerors how they manage to do so well. They may tell you that you need a short wave receiver in your car to hear the time signals on WWV and CHU; but there are many winners who use only reliable timepieces. Others insist that a calculator such as the Curta is absolutely essential. But it wasn't essential for the pair who won the American International Rally in 1959; they used a binary slide rule.

Nonetheless, the winners usually do use Curtas. At least one of these precision devices is carried by three of every five teams in major competitions. And the other two teams are probably saving their pennies toward purchase of this amazing little pepper-grinder that adds one number to another with great speed and accuracy, subtracts just as easily, and permits multiplication and division as extended adding or subtraction.

Indicating and Answering Registers Assume for a few paragraphs that you've never met a Curta. Now, as a simple example of its method of operation, consider that you have inserted the number "2" in the business-end of the machine. One turn of the crank produces the number "2" on an Answering Register, and a "1" on an Indicating Register, showing that the crank has been turned once. We could refer this to rally conditions by assuming that we were traveling at 30 mph, or 2:00 minutes for a single mile. The Curta then indicates 1 mile, 2 minutes. Turn the crank four more times and we find "5" on .the Indicating Register and "10" on the Answering Register.

There are three of these "registers": the Indicating Register, which counts the turns of the crank; the Setting Register, little lugs on the side of the Curta in which the basic problem is entered; and the Answering Register, which shows the product of the figures in the Setting Register and the turns of the crank. It is much easier to operate a Curta than to talk about it. Positioning of a lug, corresponding with digits engraved along-side the columns, governs the factor that is added with each turn of the crank. If the Setting Register is made to read "0 1 2 3 0," for example, successive turns of the crank will produce the following result:

         0 1 2 3 0
         0 2 4 6 0
         0 3 6 9 0
         0 4 9 2 0

It is a simple matter of adding the same factor over and over again. In a rally, if the time per mile were 1.230 minutes, our fourth entry above would be the time for four miles, or 4.920 minutes. A watch that read in decimal divisions of a minute, rather than seconds, would make relating to the Curta even easier, though most navigators find little trouble carrying those conversions in their minds.

But that isn't all. There are three more important points which make the Curta a fascinating tool for rally navigators. The first is that mileage can be subtracted as readily as it is added, simply by raising the axis of the crank about three-eighths of an inch and putting the gears into reverse (the crank always turns in the forward direction, can't be wound backward). Second, the entire top, or cap, of the "peppermill" can be rotated relative to the Setting Register. This is referred to as "shifting the carriage." If our example setting remains "1 2 3," it can be entered as "0 1 2 3 0 0 0." Placing a movable decimal point between the "1" and the "2," the normal reading on the Indicating Register, after the first turn of the crank, would be "1.2 3 0 0 0." But the carriage can be shifted to the right or the left, so that figures can be added or subtracted in hundreds, tens, units, tenths, hundredths, and even further, depending on the operator's needs and inclination. As an example, let us start by putting the carriage in the "third" position, allowing us room to shift two positions to the "hundredths" column. Successive turns of the crank will read thus in the Indicating Register:

	0 1 0 0
	0 2 0 0
	0 3 0 0

If the carriage is shifted to the second position, the next turn of the crank will indicate:

	0 3 1 0

And if we put the carriage in the first position and turn the crank we obtain:

	0 3 1 1

Now we raise the crank to the subtracting level and make several turns:

	0 3 1 1
	0 3 1 0
	0 3 0 9
	0 3 0 8

Each turn of the crank is therefore reducing our mileage total by one 1/100 of a mile, or 0.01. As slide-rule users know, it is an advantage to keep decimal points in their proper places, and the Curta has several movable decimal points which can be slid into position with the flick of a finger.

Curta Type II Until now we have done nothing but turn the crank and consider the Indicating Register to be showing miles and hundredths of miles. Now let us refer back to our Chapter 4 problem of 34.68 mph, which was so difficult and time-consuming with pencil and paper. We learned, either from a set of tables or by working a division problem with the Curta, that the time required to travel one mile at 34.68 mph was 1.7301 minutes. First we "clear" the machine of an previous figures, make sure the crank is in the "add" rather than the "subtract" position, and set the carriage in the third position. We then place the lugs of the Setting Register to read:

	0 0 1. 7 3 0 1

We now observe more closely the third of the Curta's registers, the Answering Dial, which shares the top of the machine with the Indicating Register. Here is an example of what happens when the crank is turned:

     3rd		0 0 1.0 0		0 0 1.7 3 0 I
     3rd		0 0 2.0 0		0 0 3.4 6 0 2
     3rd		0 0 3.0 0		0 0 5.1 9 0 3
     3rd		0 0 4.0 0		0 0 6.9 2 0 4

The time for 4.0 miles is 6.92 minutes, or about six minutes, 55 seconds. (There are six seconds in a tenth of a minute. six-tenths of a second in a hundredth of a minute.)

Should we want to get a quick reading for 23.42 miles at 34.68 mph and it's not at all unlikely that we would we do a little carriage shifting and obtain the result in this way:

     4th		0 1 0.0 0		0 1 7.3 0 1 0
     4th		0 2 0.0 0		0 3 4.6 0 2 0
     3rd		0 2 1.0 0		0 3 6.3 3 2 I
     3rd		0 2 2.0 0		0 3 8.0 6 2 2
     3rd		0 2 3.0 0		0 3 9.7 9 2 3
     2nd		0 2 3.1 0		0 3 9.9 6 5 3
     2nd		0 2 3.2 0		0 4 0.1 3 8 3
     2nd		0 2 3.3 0		0 4 0.3 1 1 3
     2nd		0 2 3.4 0		0 4 0.4 8 4 3
     1st		0 2 3.4 1		0 4 0.5 0 1 6
     1st		0 2 3.4 2		0 4 0.5 1 8 9

A quick glance shows the time to be in the vicinity of forty and a half minutes. One half minute, or 30 seconds, is 0.50 minute. but how about the remaining 0.0189? By standard practice we assume any quantity more than 5 to be the next full number, so we reduce 0.0189 to a usable nature by converting it first to 0.019, then to 0.02. Two one-hundredths of a minute equals 1.2 seconds. We can feel free to throwaway the .2 and make our final result 40 minutes and 31 seconds, or 40:31.

Anyone who uses a Curta will soon learn that there is more to it than can be told in a few pages. There is, for example, a reversing button on the side which can be made to work wonders when trying to recover after getting off course. Normally, the Curta adds both distance and time. With the crank in the subtracting position, it subtracts both distance and time. But with the crank putted out to subtract, and the reversing lug pushed down to its lower, abnormal position, the calculator adds distance and subtracts time. In use, when you turn around to retrace your route and get back on the right road, crank in time and mileage to your turnaround point in the normal manner. Then pull out the crank to its subtracting position, and lower the reversing lug. Each turn of the crank will add mileage to keep up with your odometer, but will subtract time at your established average speed. When you arrive back at the point where you went off course. the Curta will indicate the correct time for that point. Caution: return the Curta controls to normal before going on. There's no need to reset your odometer, because it corresponds with the Curta.

Just try to make up the time. Better yet, try not to get lost in the first place. The alert reader has already discovered that there is another basic way of using the Curta, and we hasten to add that it is an extremely popular method on the West Coast. All rally navigation is a matter of integrating time, speed, and distance. We have suggested using the Curta by entering the average speed in minutes-per-mile in the Setting Register. Each turn of the crank is thus equal to one mile-or ten miles, or one-tenth, or one hundredth, depending on the position of the carriage. On the West Coast they're apt to do it just the other way round, and with good results. We will let the reader make his own choice. The Western, or California, or Feldmar system, is to convert average speeds into miles per minute, starting at the first odometer Check. To use a well known example, assume that the odometer check (official mileage) is 15.5 miles, while your odometer reads 15.8 miles.

The formula is:
	S( ---- ) = CS
  S - prescribed average speed
  A - Official mileage
  B - Odometer reading
  CS - Corrected speed in miles per minute

You will note that odometer error is corrected in the use of a "corrected average speed." To work out the formula, we first multiply the official mileage of 15.5 by 6 and obtain 93. We then divide 93 into our odometer reading of 15.8 and obtain .1699. This figure .1699 can be regarded as a mileage correction factor for this rally, at least until another mileage check is given. We multiply average speeds given in the instructions by this correction factor, and obtain corrected miles per minute. If the first average speed is 40.2 mph, multiply by .1699 to obtain .6830 as the miles per minute you will use in your on-the-road computations.

Assuming that these calculations have been made with the Curta, it is now time to clear the instrument completely.

Without going to extremes of detail, you will carry time of day on the extreme left of the Mark II Curta, and distance at the extreme right hand end of the Answering Register. Each turn of the crank, with the carriage at position 3, will count as one minute, and the distance shown as the miles to be traveled in that time. By shifting the carriage to position 2, the crank will turn once for each 1/10 minute, or 6 seconds.

Provided by Bill Jonesi.

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