Digging In Battlefield Calculus

Math matters. Especially when getting it wrong means your soldiers will pay. Better get it right. Check your answers, show your work.

All military planning requires lots of math. Logistics is the obvious area, but operational planning also requires math. Today, we will explore this a bit, using the defense.

You have been tasked with defending a position. You select your engagement area, where you will destroy the enemy as the enemy attacks. Can you actually destroy the enemy before they cross it?

Step one is knowing how much time it takes the enemy to cross. If the enemy vehicles can travel 1000 meters per minute and your engagement area is 2000 meters long, you have two minutes. Ok that was easy math.

Step two is knowing how many rounds you can fire. Things start to get complicated. A good loader can help a tank crew get off a round about every four seconds, but that is not the time you can use. You need to go back to your gunnery records and look at how much time from target lock to target destroyed your crews average. It won’t be four seconds, fifteen to thirty seconds is more like it. For argument, let’s figure twenty seconds. This means a single crew can get six rounds off into your engagement area, the platoon twenty-four.

Here is where step two gets tricky. Every round isn’t always going to hit. You have to go back to your gunnery records to know your first round hit rate – which is not the gunnery score. If you were smart you broke it down into long range and short range hit rates. Say your crews have a Ph – probability of hit – of 90%. This means you need to apply this to your rounds fired.

Do you have good fire control measures? If not, you get to reduce your hits by another factor for crews shooting the same enemy vehicle. Even with excellent fire control measures, you still need to factor 10% overkill. Things get chaotic in combat. Our twenty-four rounds fired gives us nineteen hits in this scenario.

Now you need to apply your Pk – probability of kill – to your hits. Pk is based on your weapon’s ability to inflict a fatal hit to the enemy vehicle. There are some seriously tough armored vehicles out there. In a near-peer fight, the Pk isn’t going to be pretty. As a tank leader, a comprehensive understanding of Pk’s for every enemy vehicle is required. For our scenario, lets give a Pk of 75%. Now our nineteen hits only gives us fourteen kills.

How many enemy vehicles does the platoon need to destroy to stop the enemy? If we needed to destroy more than fourteen, we need to slow the enemy down to buy more time to destroy them. This is why we put out obstacles. An obstacle can easily buy another five minutes, or thirty-six kills, a huge difference. Obstacles not available? Better come up with a plan B. Artillery is a great addition, but you cannot plan on it destroying, just suppressing (artillerymen take great offense to this because artillery is nasty effective and does in fact kill and destroy).

Now for part three. This is step I was not taught, but rather learned through study. While the US doctrine taught clean battlefield calc, combat is not clean. The enemy gets a vote and has weapons also. The enemy, particularly if skilled, will apply firepower to suppress and destroy you instead of just blindly crossing the engagement area in a old school charge of the light brigade.

For fighting a well trained and well equipped enemy, you need to figure in losses. A platoon needs to plan 25%. If the enemy subscribes to the old Soviet artillery to vehicle ratio, or the enemy makes good use of support by fire positions, you can expect to take some incoming fire. That will also degrade your Ph, perhaps another 25-50%. Suddenly our fourteen kills is more like eight. With our obstacle, this drops that kill total to twenty-eight.

Now if you are able to dig in with proper triple-tier positions, those effects can be mitigated. Excellent concealment can also mitigate. A smart tanker will not want to fight the whole time from the same position, instead displacing to an alternate after just a few shots. This means you need to factor in travel time and subtract all those rounds that aren’t fired. Still, increasing your odds of survival are worth it, as long as you can still destroy the enemy before it’s bayonet time.

Part four is the hiccup. The ready rack of the tank only holds eighteen rounds. Once you expend that eighteenth round, your rate of fire drops radically as the semi-ready rack is less than ideal for feeding the cannon. This forces two major considerations. First, eighteen rounds per tank is all you get to plan for shooting in a fight. Second, you need to choose carefully what ammo selection you put in the ready rack. This decision must be based on a solid knowledge of the enemy and your cannon. Certain rounds kill certain things better. Certain rounds cannot kill certain things.

As you can see, there is a lot more to planning a defense than finding a good piece of ground and planting a shovel and a flag on it. Tank commanders still serving, may you be master mathematicians.