The Launderette problem

I once had an argument with an ex about whether it was cheaper to put all our wet clothes in one drier and run it for longer or split it between two driers and run each for less time. She thought two, I thought one. I should have known that in such heated dualistic debates there is truth in both arguments!

All the water in the clothes (above the dryness level) needs to loaded into air and removed from the dryer. First up a model of the air moisture curves from both scenarios.

Let us assume that there is a maximum water load that air through the drier can take, there is therefore a maximum rate of drying at saturation. The amount of water removed at saturation is this rate multiplied by the time at saturation.

Once the rate of evaporation of water from the clothes falls below saturation of the air then the moisture of the air will decay. I assume an exponential decay curve and some arbitrary percentage as “dryness”. The moisture in the air through the load with twice as many clothes but the same air flow one would expect to reduce at half the rate of the half-load. The area under a decay curve that starts with half some rate R is twice that of one with rate R, and also takes twice as long to reach some arbitrary level. So once the moisture falls below saturation there is no advantage to either method.

It is then easy to see that, at saturation, the remaining water (which is the same in both scenarios) will be removed in a time proportional to the amount of water. So the large load will take proportionally longer.

From this argument there is no difference between strategies. Which is easier to argue in terms of energy. The cost of any scenario is proportional to the amount of energy (electricity) put in. The length of time to dry is also proportional to the amount of energy put in, or in other words the cost.

The only variable remaining is the efficiency of drying, that is the possibility that one scenario allows for air to be “unused”. Originally I thought that putting all the clothes together increased the chance of a air coming into contact with a wet surface. However if we over-load the drier so air cannot flow between the clothes then this reduces the efficiency. On the other hand if we put just one sock in the drier then most of the air will flow through without ever coming into contact with the sock. It seems that (as usual in such arguments) we were both right and actually there is a bell curve with an optimum loading. That optimum will be around the loading where the clothes are freely spinning in the tumble drier, but not so far apart that air can pass through without good contact with the clothes.

Today is the vote for AV. First past the post is good for immediate and decisive action, but as seen in this exemplary situation above, in reality the correct action requires understanding and resolution of both sides of an argument. This is why an educated King making decisions based upon the competing input of his advisors makes the best form of government.