# The relationship betwen Equivalent Megatons and Yield

This article defines a concept called Equivalent Megatons (EMT) and gives a formula of calculating it in terms of Yield (measured in megatons).

In evaluating the destructive power of a weapons system, it is customary to use the concept of equivalent megatons (EMT). Equivalent megatonnage is defined as the actual megatonnage raised to the two-thirds power:

$$EMT = Y^{2/3}$$ where $$Y$$ is in megatons.

This relation arises from the fact that the destructive power of a bomb does not vary linearly with the yield. The volume the weapon's energy spreads into varies as the cube of the distance, but the destroyed area varies at the square of the distance.

Thus 1 bomb with a yield of 1 megaton would destroy 80 square miles. While 8 bombs, each with a yield of 125 kilotons, would destroy 160 square miles. This relationship is one reason for the development of delivery systems that could carry multiple warheads (MIRVs).

It tries to explain how the relationship arises. But I don't get how the exponent $$2/3$$ comes up. Also, what would be the unit of $$EMT$$? It feels strange. And I could not find the definition of this concept elsewhere on the Internet.

The last paragraph tries to give some example but only confuses me further. I did not get the calculation. It seems some proportional reasoning is going on. After some speculation, it seems $$160 = 8 \times 80 \times 0.125^{2/3}$$. But I could not quite make sense of it. So the above formula for EMT is calculating a measure of destroyed areas?

• The blast volume (which is proportional to the bomb's energy) is proportional to the cube of the blast radius, and the blast area is proportional to the square of the blast radius. Dec 5, 2023 at 7:19

EMT is a measure of destructive power rather than yield. When a bomb explodes it will destroy things in all directions including up and down, but for the purposes of destroying cities and stuff the metric that matters is how much surface area on the earth is destroyed, and this is what EMT is meant to quantify. It's kind of like "We don't care how big a crater this leaves in the ground, we only care about how how many city blocks are leveled"

If we model the destruction zone as a sphere and suppose that the volume of the region of space which is destroyed by a bomb is directly proportional to its yield, then mathematically the volume of destruction is related to the yield like $$\frac{4}{3}\pi R^3 \propto Y$$

From this we can see that the radius of destruction $$R$$ is related to yield as $$R \propto Y^\frac{1}{3}$$. For a bomb detonated at ground level, everything on the surface of the earth within that radius will be destroyed. Therefore the surface area of destruction is $$A = \pi R^2$$, which related to yield as $$A \propto Y^\frac{2}{3}$$ So we see that the surface cleaning power of the bomb is related to yield to the power of 2/3. EMT is defined as this quantity $$Y^\frac{2}{3}$$ as to quantify the power of a bomb in this context. Intuitively, if the EMT of a bomb is doubled then the size of area which it destroys is doubled.

• The "proportional to" instead of the "equal to" symbol clears it up so much. Thanks a lot!
– Yif
Dec 8, 2023 at 3:10

The yield $$Y$$ gives the energy released in the blast. This energy spreads in three dimensions (for example in a roughly spherical fireball) and we can take $$Y$$ as an estimate for the volume of the domain that energy spreads in, and thus the radius of that domain scales as $$Y^{1/3}$$. The destruction of an explosion happens mostly on the ground, i.e. on that two-dimensional surface we live on. You're thus interested in the area affected by the blast, which scales as the square of the radius and thus as $$Y^{2/3}$$. There's your exponent.

And then indeed the ratio of areas affected by a $$1\,$$MT blast vs a $$0.125\,$$MT blast is $$1^{2/3} : 0.125^{2/3} = 4:1$$, i.e. you need four of the smaller bombs to cover the same area and eight of them already cover double the area (160 vs. 80 square miles).

• Thanks for confirming my speculation.
– Yif
Dec 8, 2023 at 3:11