Last week I was watching the Darts world championship. I don’t usually watch darts but like a lot of people I was drawn into it by the amazing performance of 16 year old Luke Littler. Watching darts is actually pretty boring, you might as well just see the scores, in fact the only way I could get to follow the matches live without paying was via someone streaming the scores live on youtube. It’s almost the end of the holiday and the teachers are drifting in  ahead of the students. I am on sick leave/retirement so for me the holiday never ends, I have to say that it’s a good feeling.  Emma arrived back a few days ago and we had a meeting to discuss website matters. She had also been watching darts and we got talking about how accurate you have to be to score 180. To cut a short story shorter I promised to write a blog post about darts. So, what about the physics of darts. At first sight it seems fairly straight forward, just a simple projectile motion problem. Not so simple. There’s another angle to consider. The question I was interested in was what level of uncertainty is permissible in the starting conditions such that the dart hits the target but there was instantly a problem. There are three variables, 2 angles and a speed. Having said that I instantly realise that there is only one variable, the velocity, which being a vector also has direction defined by the angle, but the motion is in 3 dimensions and all our vector problems are only 2 and direction is given by an angle. How do we define direction in 3 dimensions? 2 angles? I just realised there are some more variables, we can’t assume that the launch position is always the same, this is defined by the height, distance to the board and lateral position. So that’s 6 variables! The only way forward is to vary one at a time. My idea is to make a model using Geogebra to calculate the position on the board of a dart with a certain starting condition, this now seems quite complicated but basically it’s the intersection of a plane and a parabola. I am already wondering about the reality of throwing darts, do the payers always launch at the same speed? Which of the 6 variables has the biggest impact on the final position? As usual a seemingly simple problem has turned into, I pause before saying this but decide to use the word, A NIGHTMARE.  The reason I paused was because it shouldn’t be a nightmare, these sort of problems are fun, right? They are fun for teachers but often not so much fun for students and to be honest I am starting to wish I had never promised to write a blog on this topic. Oh I just have.

I was going to leave it there and but my curiosity got the better of me and I have now spent 3 days trying to make a simulation in Geogebra. It's not as easy as it soulnds since as far as I can tell you can't draw a line graph in 3D. To get around this I plotted a series of points. I am paticularly pleased with the 3D dart. Now I can change all of the variables to see the affect that they have on the landing position. If you want to play with my simulation you can find it here https://www.geogebra.org/m/w3mfgaqf