Elephants in Stilletos

I was intending to post this yesterday but my brief intoduction to Inktober ended up taking a lot longer than planned, so I postponed this one…

Yesterday’s prompt word for Inktober was “Pressure”. As usual, I thought about several possible avenues for interpreting this prompt, one of which was the scientific definition of pressure as force over area. This reminded me of a fun fact I learned while I was at school, namely that a woman in stiletto heels will do more damage to a wooden floor than an elephant, because although she weighs a lot less than the elephant (assuming average-sized women and elephants), all her weight is concentrated over a very small area compared to the elephant’s feet.

While thinking about this yesterday, it occurred to me that this was all based on the assumption (to be fair, probably a fairly safe one) that the elephant isn’t also wearing stiletto heels. This set me off on a rare foray into cartoon-style illustration:

Probably not one of my best sketches ever, but it was quite fun to make. I also took a bit of time to do my own calculations to verify the assertion that a woman in stilettos exerts more force than a barefoot elephant.

To do this, I looked up a few figures and estimated a few others.

According to an article appearing in the Independent in 2017, the average weight for a woman in the UK is 11 stone. That’s slightly higher than I expected, but I decided to go with that figure. Converting to metric units, that’s close enough to 70kg, so we can use that for our woman’s weight.

Except that it’s actually her mass, since weight is a force (gravity) acting on a massive object (i.e. an object that has mass, not necessarily a particularly large one) and is dependent on the strength of the gravitational field it’s in. We actually need the weight for our calculation (as pressure is force/area), but that’s easy enough to calculate from the mass. Newton’s 2nd law says that force is mass times acceleration (F=ma if you like equations, as I do) and in this case the acceleration is that due to gravity. That varies from place to place around the world but it’s roughly 9.81 metres per second squared. For my rough calculations, I decided that a nice round figure of 10m/s2 would do fine. So our average woman weighs about 700 Newtons.

I didn’t make a note of where I found the figures for an elephant but apparently a female African Bush Elephant weighs on average around 3 tons. I’m not sure if that’s supposed to be long tons or short tons, but either way I decided that just calling it 3 metric tonnes (3000kg) would be close enough. Again, that’s actually the elephant’s mass (everyday language tends to be shockingly imprecise when it comes to such things), and her weight would be 30,000N using the same figure of 10m/s2 for the acceleration due to gravity. Incidentally, I decided that since our woman is (by definition) female, I’d go with a female elephant too (they tend to be a bit smaller than the males) and since I tend to think of African savannas before African forests or any part of India when thinking of elephants, I opted for an African Bush Elephant (a species that’s generally somewhat bigger than the the other two varieties).

That bit was relatively easy. Working out the areas was slightly more problematic, especially for the woman in stilettos. You will probably be relieved to hear that I don’t have any stilettos in my own shoe collection, and I was too lazy to go out and find a woman with high heels so I could measure the surface area of her heels and toes together or figure out how much of her weight would be concentrated on each part of her foot. For the initial calculation, at least, I wanted to work on the assumption that both the woman and the elephant would be standing with their weight evenly distributed across all their legs (that sounds a bit weird for the woman – obviously “all” is just “both” in her case!). A bit of online research revealed that stiletto heels usually have a diameter of no more than one centimetre, but I couldn’t find anything out about the area of the front part of the foot that would be in contact with the ground and presumably bear its share of the weight. I settled for a rough estimate of about 1cm2 for the surface area of each heel and 50cm2 for the surface area of the toe/ball of each foot. For convenience I tweaked the latter down to 49cm2, giving a total surface area of 100cm2 for both feet (heels and toes combined).

The elephant’s foot size was actually a bit easier to determine. Apparently a typical African Elephant has feet between 40 and 50cm in diameter. I decided to give the woman a bit of a helping hand by assuming our elephant had relatively small feet (hence providing less area to spread the weight) and therefore a 40cm diameter, or 20cm radius which, if we assume that the feet are circular, gives a surface area of about 1250cm2 per foot or 5000cm2 for all four feet.

To ensure our final units are correctly expressed as Pascals, or Newtons per square metre, it’s handy at this stage to convert those areas into square metres rather than square centimetres. The woman, standing with both feet firmly on the floor is putting all her 700N of weight through 0.01m2 of the floor, while the elephant’s 30,000N is being spread across 0.5m2 with the net result that the woman is exerting 70,000N/m2 or 70kPa of pressure on the floor, while the elephant is exerting only 60,000N/m2 or 60kPa. So our average woman is indeed liable to do a bit more damage to our delicate wooden floor than our average elephant, though the figures are actually quite close.

The difference gets more pronounced if they both put all their weight on a smaller area. I’m not sure how practical it would be to rest all your weight on one heel while wearing stilettos (mind you, I’m not convinced it’s very practical to wear stilettos in the first place) but suppose she’s able to do so, our woman is now channeling 700N through an area of just 1cm2 or 0.0001m2 which makes for 7MPa of pressure (that’s 7 Megapascals, 7 million Pascals or 7×106Pa if you’re not afraid of scientific notation – it’s definitely much more convenient than long trails of zeroes at either end of your numbers). Assuming that it’s enough of a challenge for our elephant to stand on just one foot, without going up on her toes or heels, she would be putting 30kN through 0.125m2, which amounts to 2.4×105Pa, which is 240kPa or 0.24MPa – significantly less than the woman on one heel.

Since my cartoon was based on the idea that an elephant wearing stilettos would do more damage to the floor than a woman in stilettos, I couldn’t leave this set of calculations without considering the pressure exerted by our elephant if she were to don a set of stiletto heels. Presumably these would have to be custom made and I’ve no idea how big they would be, nor whether she’d wear them on all four feet or just two, so let’s assume that the heels themselves culminate in points the same size as the woman’s ones, i.e. 1cm2 each and the elephant has somehow managed to contrive to stand with all her 30kN of weight bearing down on just one of these heels. That would make for a pressure of 3×108Pa, or 300MPa. As we would expect, our elephant in stilettos would do considerably more damage to any floor than our woman. It’s probably just as well that elephants are not, as far as I’m aware, in the habit of wearing stiletto heels.

I should probably add that it’s been a good few years since I last did this sort of calculation, so I hope I haven’t made any major mistakes with my units or figures, or any assumptions that are too crazy (apart from the basic premise itself, perhaps). Still, I’m fairly confident, at least that the claim made by my cartoon is fundamentally correct:

An average-sized woman in stiletto heels exerts more pressure on the floor than an average-sized elephant…

… unless, of course, the elephant is also wearing stilettos!

(Magnus Forrester-Barker, 2021-10-09)

Ink-tastic

Since I last posted, just over a month ago, I’ve been continuing to do more or less regular drawing, with both my iPad and more traditional media. As I’d hoped, my life drawing class restarted about 3 weeks ago and I’ve really enjoyed being back there. I also decided to have another go at Inktober this year.

Inktober is one of those month-long daily challenge things that seem to be all the rage these days. This particular one, as the name suggests, takes place annually in October and is based around doing daily drawing. Officially it’s supposed to be done using ink in a pen or brush (with optional pencil underdrawing), but the real purpose of Inktober according to its creator, Jake Parker, is to encourage creativity and help people to improve their skills and develop positive drawing habits, so other things such as digital art are fair game (it says so in the official Inktober faq, so that’s good enough for me). There is an official prompt list that you can follow or ignore as you see fit, and artists of all skill levels are encouraged to post their results to social media, though that is optional.

I first did Inktober in 2019 and that time I did it with black ink on white paper and mostly (though perhaps not exclusively) using a Pentel brush pen that was recommended by Jake Parker (and, as I recall, a pencil for under-drawing on a few of the days though not all that many). I stuck to the official prompt list for that year, though with loose interpretations of some of the prompts (my favourite one being “legend”, which I chose to read as “leg-end” and therefore I drew a self-portrait of my foot). All my Inktober 2019 drawings can be seen in one album on Flickr.

There is also a thing called Inktober52 which replaces the daily drawings for a month with weekly drawings for a year. I’m not sure if that first started in 2020, but that’s certainly when I first gave it a try (and the first year for which I can find a prompt list online). Unfortunately, as we all know, 2020 pretty quickly became pretty hectic and I didn’t get beyond the first 9 weeks of drawings. Still, the ones I did are available in another Flickr album. This time I again mostly worked with black ink on white paper, but with a range of different pens and occasional brushes. The sketch that ended up being my final one of the series was done in multiple colours (using non-waterproof ink and a wet paintbrush to provide a bit of blending) and I think I was intending to do a bit more work with diferent colours and quite possibly try a few other things as well.

By last October I was completely out of the habit of drawing so I don’t think I even considered doing Inktober, and it was much the same for this year’s Inktober52. However, having restarted with my drawing in the last couple of months I was keen to give Inktober another go this time round. Initially I was planning to use black ink again, but since I’m currently still trying to get to grips with using Procreate on my iPad, I decided that this would be a great opportunity to get in some extra practice and perhaps to push my explorations in directions they wouldn’t otherwise go. So for me, this year’s Inktober is being done with virtual ink. To keep more or less within the spirit of Inktober, and to provide a bit of focus, I’m restricting myself (at least initially) to the brushes within the “Inking” section of Procreate’s default brush library and mostly working in black on white, but mixing it up a little bit when the subject matter, or my personal muse, calls for other approaches.

So far I’ve managed to do one drawing every day (although I think one of them was finished slighlty after midnight) and I’m putting them all in yet another Flickr album, as well as on Instagram (where my previous Inktober/Inktober52 sketches went as well – in fact, I haven’t yet got round to using my Instagram account for anything else, although I originally set it up with the intention of sharing my Figuary 2019 portfolio there; in the end those sketches just went into one more Flickr album). All being well, I’ll reach the end of Inktober 2021 with a full set of 31 drawings (plus a few extras inspired by them) and a much better handle on how to use my current range of digital art tools.