Almost any type of navigation requires the solution of simple arithmetical problems involving time, speed, distance, fuel consumption, and so forth. In addition, the effect of the wind on the aircraft must be known; therefore, the wind must be computed. To solve such problems quickly and with reasonable accuracy, various types of computers have been devised. The computer described in this pamphlet is simply a combination of two devices: a circular slide rule for the solution of arithmetical problems [Figure 4-12], and a specially designed instrument for the graphical solution of the wind problem. [Figure 4-13]
The slide rule is a standard device for the mechanical solution of various arithmetical problems. Slide rules operate on the basis of logarithms. Slide rules are either straight or circular; the one on the DR computer is circular.
The slide rule face of the computer consists of two flat metallic disks, one of which can be rotated around a common center. These disks are graduated near their edges with adjacent logarithmic scales to form a circular slide rule approximately equivalent to a straight, 12-inch slide rule. Because the outer scale usually represents a number of miles and the inner scale represents a number of minutes, they are called the miles scale and the minutes or time scale, respectively. [Figure 4-12]
The numbers on each scale represent the printed figure with the decimal point moved any number of places to the right or left. For example, the numbers on either scale can represent 1.2, l2, 120, 1200, etc. Since speed (or fuel consumption) is expressed in miles (or gallons or pounds) per hour (60 minutes), a large black arrow marked speed index is placed at the 60-minute mark.
Graduations of both scales are identical. The graduations are numbered from l0 to 100, and the unit intervals decrease in size as the numbers increase in size. Not all unit intervals are numbered. The first element of skill in using the computer is a sure knowledge of how to read the numbers.
Reading the Slide Rule Face
The unit intervals that are numbered present no difficulty. The problem lies in giving the correct values to the many small lines that come between the numbered intervals. There are no numbers given between 25 and 30 as shown in Figure 4-14, for example, but it is obvious that the larger intermediate divisions are 26, 27, 28, and 29. Between 25 and (unnumbered) 26, there are five smaller divisions, each of which would, therefore, be .2 of the larger unit. A mental estimate aids in placing the decimal point.
Problems on the Slide Rule Face
The slide rule face of the computer is so constructed that any relationship between two numbers, one on the miles scale and one on the minutes scale, holds true for all other numbers on the two scales. Thus, if the two 10s are placed opposite each other, all other numbers are identical around the circle. If 20 on the minutes scale is placed opposite 10 on the miles scale, all numbers on the minutes scale are double of those on the miles scale. This feature allows one to supply the fourth term of any mathematical proportion. Thus, the unknown in the equation could be solved on the computer by setting 18 on the miles scale over 45 on the minutes scale and reading the answer (32) above the 80 on the minutes scale. It is this relationship that makes possible the solution of time-speeddistance problems. This can also be solved algebraically:
Time, Speed, and Distance
An aircraft has traveled 24 miles in 8 minutes. How many minutes are required to travel 150 miles? This is a simple proportion which can be written as:
Setting the 24 over the 8 on the computer as illustrated in Figure 4-15 and reading under the 150, the answer is 50 minutes.
A problem that often occurs is to find the GS of the aircraft when a given distance is traveled in a given time. This is solved in the same manner, except the computer is marked with a speed index to aid in finding the correct proportion. In the problem just stated, if 24 is set over 8 as in the original problem, the GS of the aircraft, 180 knots, is read above the speed index, as shown.
Problem: GS is 204 knots. Find the distance traveled in 1 hour 15 minutes.
Solution: Set the speed index on the minutes scale to 204 on the miles scale. Opposite 75 on the minutes scale, read 255 NM on the miles scale. The computer solution is shown in Figure 4-16. The solution for time and speed when the other variables are known follows the same basic format. [Figures 4-17 and 4-18]
Since 1 hour is equivalent to 3,600 seconds, a subsidiary index mark, called seconds index, is marked at 36 on the minutes scale of some computers. When placed opposite a speed on the miles scale, the index relates the scales for converting distance to time in seconds. Thus, if 36 is placed opposite a GS of 144 knots, 50 seconds is required to go 2 NM; and in 150 seconds (2 minutes 30 seconds), 6.0 NM are covered. Similarly, if 4 NM are covered in 100 seconds, GS is 144 knots. [Figure 4-19]
Conversion of Distance
Subsidiary indexes are placed on some computers to aid in the conversion of distances from one unit of measure to another. The most common interconversions are those involving SM, NM, and kilometer (km).
Statute Mile-Nautical Mile Interconversion
The miles scale of the computer is marked with a SM index at 76 and a NM index at 66. The units are interconverted by setting the known distance under the appropriate index and reading the desired unit under the other.
Example: To convert 136 SM to NM, set 136 on the minutes scale under the STAT index on the miles scale. Under the NAUT index on the miles scale, read the number of NM (118) on the minutes scale. [Figure 4-20]
Conversion of NM or SM to km
A km index is indicated on the miles scale of the computer at 122. When NM or SM are placed under their appropriate index on the miles scale, kms may be read, on the minutes scale, under the km index.
Example: To convert 118 NM to kms, place 118 on the minutes scale under the NAUT index on the miles scale. Under the km index on the miles scale, read km (218) on the minutes scale.
Multiplication and Division
To multiply two numbers, for example 12 × 2, the index (printed as 10 on the minutes scale) is placed opposite one of the numbers to be multiplied (12), and the product (24) is read on the miles scale above the other number (2) on the minutes scale. [Figure 4-21]
To divide one number by another, for example 24/8, set the divisor (8) on the minutes scale opposite the dividend (24) on the miles scale, and read the quotient (3) on the miles scale opposite the index on the minutes scale. [Figure 4-22] In the computations encountered in air navigation, as in the above examples, a mental estimate aids in placing the decimal point.