7M198 Howitzer: Shell HE M107 shell: High-explosive Weighs 95 pounds 50 m destructive radiusGun has max. range of 24,000 m (14.9 miles) and max. rate of 4/minute with this shell
8M198 Howitzer: Gun CrewGun crew uses firing tables to set angle and muzzle velocityAngle adjusts from 4° below horizon to 72° above11 standard velocities, set by number of gunpowder bags and/or type of power grain; muzzle speed for this shell ranges from 208 m/s to 684 m/s (465 mi/h to 1,530 mi/h)
10M198 Howitzer: Firing Table Range in metersElevation in mils (6400 mils = 360°)Fuze setting for a level (graze) burst at standard rangeChanges to decrease the height of the burst level by 10 metersHow much the range changes for each 1 mil change in elevationAmount of elevation change to achieve a change in range of 4x the probable errorTime of flight in secondsDrift correction in mils due to shell spin; US guns have right-hand rifling that makes shells drift rightCorrection for each knot of crosswind (1 knot = 1.15 mi/h)
11M198 Howitzer: Firing Table Range in meters10-19) RANGE CORRECTIONS FOR:10-11) 1 m/s decrease or increase in muzzle speed12-13) 1 knot headwind or tailwind14-15) 1% decrease or increase in air temperature from US Standard Atmosphere16-17) 1% decrease or increase in air density from US Standard Atmosphere18-19) 1 “square” decrease or increase in projectile weight
12M198 Howitzer: Theory vs. Reality In the BHS AP Physics B course we derive this formula for range over level ground:How well does that formula work with the real gun, firing a shell at 376 m/s?Formula says max. range is at sin(2θ)=1, so at 45°Firing table shows max. range is at 44.4°2. Formula says max. range is 14,400 m2. Firing table shows max. range is really 9,874 m due to air resistance, etc.
13M198 Howitzer: Theory vs. Reality Our “vacuum” range formula:The chart shows range vs. θ for the formula (dashed line) versus the real gun’s firing table (solid line):
14Calculating Firing Tables Obviously firing tables are crucial to using such weapons. Computers have always been used to calculate the complex differential equations.For centuries, “computers” were people. Human computers date back to an effort in 1757 to calculate an orbit of Halley’s comet such “computers” calculated firing tables for the U.S. in World War I.In 1940 the “computer” was the woman, not the machine
15Calculating Firing Tables During World War II, the army built ENIAC, the first general-purpose electronic digital computer to compute firing tables.Occupying 1800 square feet, ENIAC—the Electrical Numerical Integrator and Computer—weighed 30 tons, used 160,000 W of power, and had 17,500 vacuum tubes. Calculations that took a human computer 12 hours to perform were done in 30 seconds by ENIAC. It was also used for atomic bomb calculations.
17Calculating Firing Tables ENIAC was less powerful than a modern-day hand-held calculator.Computers use many, many switches to do their work; ENIAC’s switches were the 17,500 vacuum tubes.The hot tubes burned out so fast that it could only operate about 6 hours before needing repairs.Old vacuum tubes and resistors did the switching
18Calculating Firing Tables Today, vacuum tubes are still used in microwave ovens.In computers they have been replaced by transistors. A modern-day chip has millions to billions of transistors.Hundreds of modern transistors will fit into a single red blood cell.Microwave magnetron (sliced open)
19non-commercial use when attributed to Granger Meador All source materials are being used under “fair use” provisions of the Copyright Act for educational purposes.Primary Source:Day, Michael A. & Walker, Martin H. (1993, March). Experimenting with the National Guard: Field Artillery Gunnery. The Physics Teacher (31)3, ppThis presentation is Creative Commons licensed for free distribution fornon-commercial use when attributed to Granger MeadorInquiry Physics