Unit 4: Projectiles Inquiry Physics The M198 Howitzer.

Unit 4:Projectiles

Inquiry Physics

www.inquiryphysics.org

The M198 Howitzer

M198 155mm Howitzer

Photo from Field Artillery Journal, Ft. Sill, Oklahoma

Used since 1979 by US Army and Marines; soon to be replaced by a lighter unit

• 15,800 pound gun

• 155 mm diameter barrel

• Cost: $527,000

• Various shells (including nuclear); we’ll look at the most common one

M198 Howitzer: Description

M198 Howitzer: Operation

M198 Howitzer: Firing

M198 Howitzer: Firing

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

M198 Howitzer: Shell

• 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)

M198 Howitzer: Gun Crew

M198 Howitzer: Firing Table

1) Range in meters

2) Elevation in mils (6400 mils = 360°)

3) Fuze setting for a level (graze) burst at standard range

4) Changes to decrease the height of the burst level by 10 meters

5) How much the range changes for each 1 mil change in elevation

6) Amount of elevation change to achieve a change in range of 4x the probable error

7) Time of flight in seconds

8) Drift correction in mils due to shell spin; US guns have right-hand rifling that makes shells drift right

9) Correction for each knot of crosswind (1 knot = 1.15 mi/h)

M198 Howitzer: Firing Table

1) 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

M198 Howitzer: Firing Table

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?

1. Formula says max. range is at sin(2θ)=1, so at 45°

1. 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.

M198 Howitzer: Theory vs. Reality

The chart shows range vs. θ for the formula (dashed line) versus the real gun’s firing table (solid line):

Our “vacuum” range formula:

Calculating Firing TablesObviously 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. 70 such “computers” calculated firing tables for the U.S. in World War I.

In 1940 the “computer” was the woman, not the machine

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.

Calculating Firing Tables

ENIAC

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

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)

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. 136-143.

Inquiry Physics

www.inquiryphysics.org

This presentation is Creative Commons licensed for free distribution for

non-commercial use when attributed to Granger Meador