This is a pretty cool video. This guy starts with just a simple tool and digs a giant hole in the ground. From this hole, he makes a small swimming pool and a little underground room. But damn—how long would it take to make this? The video is only 20 minutes long, but surely it must take much longer than that to build the pool-house thingy.

How about an estimate? Let’s estimate how long it would take a mostly normal human to dig this out. This is a great example of the power of estimations. I don’t need to get an exact value (and if it was exact, it wouldn’t really be an estimate). However, if I get a build time of 10 hours that seems like something I could do. A build time of 1,000 hours would take one person months to build. OK, let’s do this and see what we get.

There are couple of parts to this estimation. First there is the volume. What is the volume of dirt that needs to be removed? This isn’t a terribly difficult estimation. I just need the length, width, and height of the hole to calculate the volume. Second is the volume per “scoop.” Notice that the guy digs for a bit and then gathers the debris to throw it out. If I know the volume and the time per scoop, I can find the number of scoops and therefore the total dig time. That’s the plan.

I am going to start with total volume since that’s the simplest. Looking at the video, it looks like it has an average depth of 2 meters with a length of 4 meters and a width of 3 meters. That puts the total volume at 24 cubic meters. Don’t worry, I am going to include my calculations as a python code below so that you can make your own estimations.

Now for the scoop volume and time. Suppose I just consider the volume in one single “toss.” This is approximately a flat cylinder of dirt. Just using my own hands, I’m going to say the diameter of this dirt is around 20 cm with a depth of 10 cm (both are on the large side of my estimation). If I convert these values to meters, I can use the following equation for the volume of a cylinder.

With my estimates, I get a dirt toss volume of 3.14 x 10^{-3} m^{3}. If that seems small, it’s because it is. Remember, 1 cubic meter is a box that is one meter long on each side. So, how many scoops would it take to get the whole thing dug out? The number of scoops is just the total volume divided by the volume of one scoop. That’s 7,639 scoops.

What about the time? Let’s break this dirt toss into three parts. First, the digging. Second, the scooping. Third, the throwing the dirt out of the hole. This third part could involve some moving around also (so that you can get to the edge of the hole). Looking at the video, I get the following estimated times for one scoop:

- Dig time = 10 seconds.
- Scoop time = 6 seconds.
- Toss time = 3 seconds.

This gives the total time for one scoop-toss at 19 seconds. I think that is very generous. Now I just need to multiply the number of scoops and the time per scoop. This puts the total dig time at 1.45 x 10^{5} seconds or 40 hours. Yes, that’s a full work week. No overtime.

Like I said, here are my calculations (in case you want to change them).

But now for the original question that I had. Is this even possible for one person? Did this dude really dig out the hole and do everything by himself? I’m going to say it’s possible. He could do this in one week. OK, maybe it would take 3 weeks or maybe just 4 days if you have different estimates. It’s going to clearly take more than just one day. My guess is that this was completed over a couple of days, but I suspect he had help from some other people. But it’s entirely plausible he did it himself.

Now you can see the power of an estimation. It’s not difficult and you can get a very rough answer. Rough answers can still tell you quite a bit about a problem. In this case, I might go ahead and get a more accurate dig time value if I wanted to build one of these pool-house things myself. If my estimate had been 1,000 hours, I would just walk away.

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