722 SCHOOL SCIENCE AND MATHEMATICS

Finally, students react favorably to actual equipment whetherin full working order or not. Have a specific idea, tell it to yourfriends and associates, and above all keep your eyes open forsources of supply. You will be surprised at how quickly you willhave a collection of suitable items.

MATHEMATICS HELPS OUR AERIAL DEFENSE

LESTER DAWSONUniversity of Alaska j College, Alaska

Faster and faster we wing the skies. Today the key word inwar is speed. Consider two pursuit planes traveling toward eachother at the rate of 350 miles per hour. TicI^, tock! and theP-40’s are about three city blocks closer to each other. The highspeeds of modern warfare make it more dependent upon mathe-matics than ever before. Yesterday the command was "Firewhen you see the whites of their eyes!’-3 Now we fire at the enemyby means of observations and computations�even before wecan see them.

Victory through air force superiority implies the use of severaltechnical skills, of which mathematics is one. In the next fewmoments, I will mention some of the uses of mathematics in thedesigning of powerful planes, in the bombing of enemy objec-tives, and in the firing of anti-aircraft guns.

Swifter planes have been designed by aeronautical engineersthrough the study of streamlining. About five years ago, an air-plane company in Southern California offered $12,000 for themathematical solution of a certain differential equation dealingwith streamlining. This inducement led to a solution that gavea much more effective airplane wing.

Often when a more sturdy, air-worthy ship is designed, it isbecause of some new discovery in the strength of materials, orto some new application of the principles of stress analysis. Bothof these technical fields of engineering are highly mathematicalin their nature.

. . . Listen! There goes a roaring B-26 to scout the enemyarea. On the bomber a movie camera is mounted to take photo-.graphs of the area covered. The aerial photogrpah is to servetwo purposes: It is used to detect enemy information, such ascommunication lines, harbors, war-craft factories and other mili-tary objectives. The photograph is also to be used to make maps

MATHEMATICS HELPS OUR AERIAL OFFENSE 723

of the enemy-infested area, so that tactics against the foe can beplanned. The principles of trigonometry are used to determinethe scale of the aerial map. The addition of a north and southline and a military grid system of lines completes the map. Thusthe homeward bound B-26 returns with data for a valuable mili-tary map of the enemy area.The best defense is a good offense. By the use of a map of the

enemy area and other pertinent military information, plans arecarefully made for an air attack. The B-26 again roars in theskies.�Hours later, the sleek bomber sights its objective anddischarges its deadly cargo. When the plane is directly over thetarget below, the bombs will hit their objective. This means thatnearly four miles before the plane reaches the target, the bombsmust be released. Just when they should be dropped is a com-plex problem that must be solved by considering the speed andaltitude of the plane, the direction and velocity of the wind andother atmospheric conditions. This problem is solved by theskillful use of the automatic bomb sighter.When we weaken our enemies by air raids, w^ must expect air

attacks from them. Effective air defense is maintained by lo-cating good anti-aircraft gun equipment in strategic spots. Suc-cessful firing of the anti-aircraft gun depends upon knowing thealtitude of the enemy plane, the speed of the moving target, andboth the direction and angle of elevation of the attacking plane.From these quantities are computed the data for aiming at themoving target, also the time setting for the fuse that will causethe shell to burst in the vicinity of the target. A data computeroperated along with an automatic range finder solves the prob-lem almost instantly. The gunner is also helped by firing charts,which take into consideration such quantities as wind velocity,muzzle velocity of the bullet, atmospheric density, humidity,barometric pressure, temperature at the gun, powder tempera-ture, weight of the bullet, and drift caused by wind. The man atthe gun is further aided by trajectory charts, which show thetime setting of the fuse for various angles of elevation. The gun-ner fires the huge gun! An unfriendly bomber is crippled. Hefires again. This time the raider is hit. A blazing mass streaksthe skies. Seconds later, an enemy plane crashes to its doom!

Victory through air force�yes. Victory�through out-match-ing our enemies by our fast moving planes and our rapid firingguns. Victory through our skillfully trained men, both in ouraircraft factories and on the battle field.