Making the fuel go further

 

A couple of weeks ago The Guardian published some tips on coping with the soaring petrol prices. One suggestion was to stop driving at 80mph on the motorway but drive at 70mph instead, making a 20% saving. That's no use to me: it's illegal to drive at 80mph so I don't. But I was interested in where the statistic came from. I was going to do a full calculation based on the drag equation but then it occurred to me that when comparing between two speeds, the other terms should be the same and I just need to consider speed. I am, of course, assuming that all fuel consumption is proportional to drag. Drag is proportional to speed-squared. So I did 80^2/70^2 and got 1.31 so the fuel use at 80mph would be 1.31x higher than that at 70mph. So isn't it a 30% reduction? I normally do percentage difference as difference/true answer. In this case it might be (80^2-70^2)/80^2 = 23%, being 23% of what it WAS at 80mph. That's probably where the figure came from. Now trying a reduction from 70mph to 60mph, I get a 27% reduction! But I remember from the oil shock of the 1970s that 55mph is said to be the most fuel efficient speed. This site gives some figures to consider.

Rigs of Nigg

 

There's a wonderful programme on the engineering and social challenges of the oil rig production at Nigg available until August https://www.bbc.co.uk/iplayer/episode/m000yybp/rigs-of-nigg

Calculating the percentage yield for carbon dioxide

 I surprised myself by working out a fairly obvious way of working out percentage yield in a chemical reaction. We weighed out 2 grams of marble chips and added 40 cubic centimetres of 1M hydrochloric acid. The reaction produces carbon dioxide so we weighed the whole conical flask at the start and then at the end. It had got lighter because the carbon dioxide escapes into the air. 

By using relative formula mass we could calculate the expected mass of carbon dioxide and compare it with the actual mass, thus allowing percentage yield to be calculated.

Ca' the yowes to the knowes

 

There was a shepherd calling a sheepdog in Langdale which reminded me of Robert Burns' song. More to the point, there was a clearly discernible echo from Pike Howe crags. Map measurements suggest that direct sound came from 100m away (red arrow) and that the reflection travelled 150m there and 250m back. The difference is 300m of sound travel. That gives about a second which would be noticeable as an echo. I think it might have been less but it is hard to tell which part of the crag is reflecting the sound. The yowes ended up on the Howe in this case.

Phase difference in the shadows

 

The shadow pattern for the beads on this blind attracted my attention. The beads almost hang in a sine curve. With the shadow, you can detect phase difference. A shows a phase difference of pi radians (180 degrees) because when the shadow peaks, the beads are in a trough. At B the phase difference is pi/2 radians (90 degrees) - when one peaks the other is at equilibrium. C is an entirely positive curve and not unreminiscent of the kinetic energy graph for the motion.

Why sunlight is less intense if it hits at an angle

 

Look at the image of the Ukraine flag on the floor. It is much bigger than the size of the original on the window and yet the same light that passed through the original is present in the image on the floor. No extra light has appeared to make it bigger. So the same energy is spread over a bigger area - the intensity is reduced. This has happened because the light hits the floor at a more acute angle.

More thoughts on radiation dose and non-stochastic

 

The sun's been out and I've been trying to get a tan. I spent hours in the hills yesterday but you can't tell. This got me thinking about what radiation dose means, based on what I read on the website I linked in 2 days ago. I was wondering whether low intensity but for hours equals a high dose like high intensity for a few minutes. Maybe the sum of the energy will be the same but not the effect. That's probably at the root of the stochastic/non-stochastic distinction. Low intensity may not burn but there is a very low chance of genetic damage. The longer I go on, that is the only effect. But in mid-summer at higher intensity, I can burn in 10 minutes. That's a non-stochastic effect.