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**The M198 Howitzer Unit 4: Projectiles Inquiry Physics**

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M mm Howitzer Used since 1979 by US Army and Marines; soon to be replaced by a lighter unit Photo from Field Artillery Journal, Ft. Sill, Oklahoma

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**M198 Howitzer: Description**

15,800 pound gun 155 mm diameter barrel Cost: $527,000 Various shells (including nuclear); we’ll look at the most common one

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M198 Howitzer: Operation

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M198 Howitzer: Firing

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M198 Howitzer: Firing

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**M198 Howitzer: Shell HE M107 shell: High-explosive Weighs 95 pounds**

50 m destructive radius Gun has max. range of 24,000 m (14.9 miles) and max. rate of 4/minute with this shell

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M198 Howitzer: Gun Crew Gun crew uses firing tables to set angle and muzzle velocity Angle adjusts from 4° below horizon to 72° above 11 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)

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**M198 Howitzer: Firing Table**

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**M198 Howitzer: Firing Table**

Range in meters Elevation in mils (6400 mils = 360°) Fuze setting for a level (graze) burst at standard range Changes to decrease the height of the burst level by 10 meters How much the range changes for each 1 mil change in elevation Amount of elevation change to achieve a change in range of 4x the probable error Time of flight in seconds Drift correction in mils due to shell spin; US guns have right-hand rifling that makes shells drift right Correction for each knot of crosswind (1 knot = 1.15 mi/h)

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**M198 Howitzer: Firing Table**

Range in meters 10-19) RANGE CORRECTIONS FOR: 10-11) 1 m/s decrease or increase in muzzle speed 12-13) 1 knot headwind or tailwind 14-15) 1% decrease or increase in air temperature from US Standard Atmosphere 16-17) 1% decrease or increase in air density from US Standard Atmosphere 18-19) 1 “square” decrease or increase in projectile weight

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**M198 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 m 2. Firing table shows max. range is really 9,874 m due to air resistance, etc.

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**M198 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):

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**Calculating 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

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**Calculating 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.

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**Calculating Firing Tables**

ENIAC

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**Calculating 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

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**Calculating 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)

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**non-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, pp This presentation is Creative Commons licensed for free distribution for non-commercial use when attributed to Granger Meador Inquiry Physics

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