This week we dived into the thrilling world of **approximate calculations**! You may think that I type this sarcastically, but I do not, it really was actually quite fun!

Your first question is likely what are approximate calculations? Well I’m very glad you asked. Approximate calculations are essentially calculations that are carried out before you really have all, or sometimes any of the exact data. They are calculations based on assumptions and simplifications.

You may therefore wonder what the point is? Why do an approximate calculation if it’s not going to give you an exact value?

The answer is that sometimes you don’t want or need an exact answer. Sometimes you just want the jist. Sometimes you just want to know, roughly, if something will work. These calculations are used when you want to check the feasibility of something before you’ve really started to design it, it’s a starting point and in some sad cases it reveals a dead end.

Some of the questions we looked at were things like how much land would you need to dedicate to farming biomass if you hoped to run all the worlds air travel of it? The answer? Roughly 1/6th of the worlds land mass. We also looked into how tall a conical pile of the entirety of the worlds population would be… A bit morbid, but there you go.

**What these questions demonstrated is that when it comes to quite abstract problems, and real life representations of values we often find it really difficult to foresee the correct answer. In particular we struggle visualising volumes.**

As a wee bit of fun I’m going to do some approximate calculations of my own…

**If Voldemort is attempting to kill you, how long do you have to get out of the way of the killing curse?**

Lets first assume that a spell acts in a physical sense, like light (based on the films). Thus the spell will travel at (3×10^8)m/s.

Next we need to approximate how far away you are likely to be standing from Lord Voldemort when he strikes. I would say, around 2m, but taking off the length of his arm, assuming he has extended it fully to curse you, lets say 1.6m. So, assuming all this and since s=d/t, you would have 1.6/(3×10^8)=(0.5×10^-8)s to get out of the way… Potentially problematic.

Granted that was a very easy question, perhaps we should look at something a bit more complicated, such as;

**2.Is it more environmentally friendly for me to get the ferry back to Northern Ireland for the holidays or the plane?**

Stats:

*The ferry requires a 2 hour bus journey from Glasgow to Cairnryan and then a 2 and a half hour ferry crossing to Belfast.*

*The plane requires a half hour bus journey to the airport and a 25 minute flight to Belfast City.*

My first assumption will be that every mode of transport I am in is at capacity.

Since both modes currently use fossil fuels I’m going to calculate the energy required for each journey and assume that the one with the most energy consumption is the worse one.

Starting with the plane. Taking it to be an easyjet flight we can assume that it will be an Airbus A319. This plane has a capacity of 144 seats and uses 2.93kg/km and the distance between the airports is around 180km.

After a bit of rounding we can say the plane will use 520kg (2.93×180≈3×180=520) of fuel during the flight which is roughly** 3.7kg per seat (520/144≈520/140=3.7).**

The specific Energy value for jet fuel is 43.2MJ/kg, so multiplying this value by the weight per seat we can calculate the energy used per seat. **43×3.7≈43×4=172MJ.**

Next we can move onto the ferry, we shall work under the assumption that it is a Steneline, Superfast ferry. Knowing the maximum power supplied by the Ferries engines and the time taken to complete the journey we can use the equation E=Pt, to find the energy used by the Ferry. **(46000x(2.5x60x60))=414MJ.**

The numbers for the ferry’s capacity are harder to find on account of their being so many different kinds of capacity. For example car capacity doesn’t mean passenger capacity. The values given range from 626 to 1200, thus I will take 1000 to be an average number of passengers on board. Meaning that the energy per passenger becomes, **414/1000=0.4MJ.**

At this point it is pretty clear that the ferry is the most energy efficient form of transport, however just to be sure we’ll now take a look at the bus journeys that go with each mode.

Working on a value from a Canadian bus website we shall assume the same amount of energy per passenger for both types of bus, which is 0.32MJ/km.

To get to the ferry terminal the bus must travel 79 miles which is 127km. The energy used is therefore,** 127×0.32≈130×0.3=39MJ/km.**

To get to the airport on the other hand a mere 10 mile trip is required which is, 16km. Thus, the energy required is** 16×0.32≈16×0.3=4.8MJ.**

**The total energy for the ferry is therefore, 39+0.4=39.4MJ, whereas the total value for the plane is 4.8+172=176.8MJ.**

So after all that we can be sure that despite how much longer it takes it is much more energy efficient to get the ferry across the Irish Sea than to hop on a plane!