Hokay:
1m long and 10cm diam rod of tungsten massing 150Kg moving at mach 18 (6125m/s) will have the KE of .68Kilotons or 1.36 million lbs of TNT.
2m long and 10cm diam rod of tungsten massing 300Kg moving at mach 18 (6125m/s) will have the KE of 1.36Kilotons or 2.7 million lbs of TNT.
I suspect these estimates are conservative, since the projectiles would have a Cd closer to that of .04 (streamlined) than of .5 (cone)
For a single human, this is the very definition of overkill.
I did the calcs for a MBT gun KE penetrator first to get the method down. You're talking 5900 lbs of TNT more or less.
There was a time I could have done hte calcs knowing the orbital vel, altitude, air density, horizontal displacement of the target, etc. Been a while since I have done rocket science.
For KE Tank Round (wiki data)
Variable / Unit / Assumptions / Etc Symbol Value Units Notes
Velocity @ Impact v 1740 m/s
radius r 0.015 m
length or height h 0.6 m
volume vol 0.0004239 m^3 h(pi*r^2)
densityU dU 19.1 g/cm^3
densityU dU 19100 Kg/m^3 1Kg/m^3 = 1000g/cm^3
densityW (tungsten) dW 19.25 g/cm^3
densityW (tungsten) dW 19250 Kg/m^3
Mass U Penetrator Mu 8.10 Kg dU*vol
Mass W Penetrator Mw 8.16 Kg dW*vol
Kinetic Energy @ Impact U KEu 1.23E+07 joules .5*mv^2
Kinetic Energy @ Impact W KEw 1.24E+07 joules .5*mv^2
Kiloton TNT KtTNT 4.18E+09 joules
Kinetic Energy @ Impact U KEu 2.93E-03 KtTNT
Kinetic Energy @ Impact W KEw 2.95E-03 KtTNT
Kiloton Kt 2000000 Lbs
Kinetic Energy @ Impact U KEu 5858.73 LbTNT 5858 lbs of TNT
Kinetic Energy @ Impact W KEw 5904.74 LbTNT 5904 lbs of TNT
For 1m Rod Dropped From LEO
Variable / Unit / Whatever Symbol Value Units Notes
Start Orbit Height Ho 150000 m 150Km
Start Velocity Minimum Vo 7814 m/s Low Earth Orbit at 150Km
Rod Radius Rr 0.05 m 10 cm diameter
Rod Length h 1 m sad attempt to make calcs easier
Rod Frontal Area A 0.00785 m^2
Rod Volume vol 0.00785 m^3
Rod Mass Mrod 151.1125 Kg/m^3 Tungsten, baby, cause its more dense
densityW (tungsten) dW 19250 Kg/m^3
Rod Coeff Drag Cd 0.04 none Streamlined body
Start KE in Orbit KEo 4.61E+09 joules Starting off 2 orders of magnitude greater than KE penetrator
Velocity at Impact Vt 18 mach mach = 340.3 m/s @ 15degC
Velocity at Impact Vt 6125.4 m/s Very conservative, given a cones Cd = .5
Kinetic Energy @ Impact W KEw 2.83E+09 joules
Kiloton TNT KtTNT 4.18E+09 joules
Kinetic Energy @ Impact W KEw 0.68 KtTNT
Kiloton Kt 2000000 Lbs
Kinetic Energy @ Impact W KEw 1,355,120 LbTNT 1.36 million pounds of TNT
For 2m Rod Dropped From LEO
Variable / Unit / Whatever Symbol Value Units Notes
Start Orbit Height Ho 150000 m 150Km
Start Velocity Minimum Vo 7814 m/s Low Earth Orbit at 150Km
Rod Radius Rr 0.05 m 10 cm diameter
Rod Length h 2 m Double length of rod
Rod Frontal Area A 0.00785 m^2
Rod Volume vol 0.0157 m^3
Rod Mass Mrod 302.225 Kg/m^3 Tungsten, baby, cause its more dense
densityW (tungsten) dW 19250 Kg/m^3
Rod Coeff Drag Cd 0.04 none Streamlined body
Start KE in Orbit KEo 9.23E+09 joules Starting off 2 orders of magnitude greater than KE penetrator
Velocity at Impact Vt 18 mach mach = 340.3 m/s @ 15degC
Velocity at Impact Vt 6125.4 m/s Very conservative, given a cones Cd = .5
Kinetic Energy @ Impact W KEw 5.67E+09 joules
Kiloton TNT KtTNT 4.18E+09 joules
Kinetic Energy @ Impact W KEw 1.36 KtTNT
Kiloton Kt 2000000 Lbs
Kinetic Energy @ Impact W KEw 2,710,239 LbTNT 1.36 million pounds of TNT