Nov 13, 2010

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Calculating the maximum heel size for Lady Gaga’s shoes


I get all my news from Fox News, especially important science news. Like the height of the Lady Gaga’s shoes and the news that playing Tetris is good for me. Fox News is the only network I know that will break the presidential address to announce important breaking story that like “Paris Hilton was spotted wearing sun glasses today.” Their news reporting is unparalleled.

So I spotted this story about Lady Gaga’s shoes on Fox News.

The physicist in me wondered: how high can Lady Gaga’s heels be? Turns out, there’s a formula for that. Physicists at the Institute of Physics (London, UK) have devised a formula that high-heel fans can use to work out just how high they can go. Based on your shoe size, the formula tells you the maximum height of heel you can wear without toppling over or suffering agonies.

h = Q x(12+3s /8)

h is the maximum height of the heel (in cm)
Q is a sociological factor (see below to work this out)
S is the shoe size (UK ladies sizes). This factor makes sure that the base of support is just good enough for an experienced and sober, high-heel wearer not to fall over.

‘Q’ is defined as follows:

Q = ———————————-

The variables are:

p – the probability that wearing the shoes will help you ‘pull’ (in a range from 0 to 1, where 1 is sexy high and 0 is stick to carpet slippers). If the shoes are a turn-off, there’s no point wearing them.

y – the number of years experience you have in wearing high heels. As you become more adept, you can wear a higher heel. Beginners should take it easy.

L – the cost of the shoes, in pounds. Clearly, if the shoe is particularly expensive, you can put up with a higher heel.

t – the time since the shoe was the height of fashion, in months (0 = it’s the ‘in thing’ right now!). One has to suffer for one’s art, and if the shoes are terribly fashionable, you should be prepared to put up with a little pain.

A – units of alcohol consumed. If you’re planning on drinking, be careful to give yourself a little leeway for reduced coordination.

Lets see if we can apply this to lady Gaga.

P=1 – How sexy one would look. Well, these would really be sexy in a video.

y=10 – number of years in a high heels – I think she has been doing this for 10 years

L=1,000 cost of the shoes in UK pounds. (off the shelf shoes cost $250 (150 pounds), so the 1,000 pounds for custom shoes by Alexander McQueen sounds right; this is not a critical number)

t= -0.5 How long has it been since these shoes became popular. Yes, a negative number since it will come in to fashion at a future date when the music video comes out.

A=0 Amount of Alcohol. Lady GaGa drink alcohol? Never. She has a disreputation to uphold. She might do Coke but not alcohol…

So Q= 1(10+9)(1000)/(0.5)(1)(20)(1020) = 1.86

She is 5’1″, and apparently wears size 5.5 shoes. (Too many unreliable sources, but 5.5 is the consensus). We need to convert this to UK size. (chart here)

US shoe size 5.5 is sale as British size 3.

So h=Q x(12+3s /8)= 1.86x(12+3(3)/8) = 23.6 cm = 24.4/2.54 inches = 9.6 inches.

As the Fox News informed me, the size of her heels were 10 inches..

Amazing… Physics Rules…

What keeps lady Ga Ga from falling over while wearing 10 inch heels? Physics – of course.

For lady Gaga, with billion Youtube views of her videos, the Q factor can be pretty close to -1, so she can technically wear shoes with infinitely high heels.

Sep 26, 2008

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Friday Fermi Problem: How much does a barrel of Gold cost? $1M? $10M? $100M?


Recently I was listening to the news and the broadcaster was giving numbers on the price of a barrel of oil and and an oz of gold.

Oil is very often referred to as “black gold”, so I started to ponder about the price of a barrel of gold.

You might think that this is a simple multiplication problem, and you are right, it is. But without using a calculator and without searching google, can you do this? Can you come up with an approximate number?

We are just looking for an order of magnitude calculations.

Make a guess, is it $1M, $10M, or $100M?

So with an able 9 year old assistant, who likes to do multiplications, this is what we came up with.

For starters, the broadcaster told us that the gold is at $1,000 per oz.

A barrel is 42 US gallons; but approximate it to 40 gallons.

1 oz is about 31 grams, but approximate it to 30 grams.

The price of gold is given in terms of the weight but the problem asks for the value based on volume, so one needs to do a conversion.

Sigh.. we will have to do this in metric units!

40 gallons is about 150 liters.

Density of gold is about 20 g/cc

So 30 grams of gold is 1.5 cc.

1 liter is 1000 cc

150 liters is 150,000 cc and 1.5 cc of gold costs $1000.

Hence the total cost of a barrel of gold is

(150,000/1.5)* $1000 = 100,000x$1000 = $100M

Really? $100M? that doesn’t sound right. That’s way too high.

Did we miss any zeros?


Let us double check. How much does a gold bar in Fort Knox cost?

gold bars are about 400 oz. So each gold bar costs about $400k. If you just do a visual comparison, can a barrel accommodate 250 bars?

A typical bar at Fort Knox is 7″x3.5″x1.75″, lets call it 7″x4″x1.5″ approximately.

Barrel is about 30 inches in height and 20 inches in diameter.

So if you try to visualize it, you can put a stack of 20 gold bars and can fit about 10 to 12 of those stacks in a barrel, so it sounds right.

So a barrel of gold costs $100M! Vow.

I know it is right, but I still can’t believe it.

Corollary: If you see a movie of thieves carrying bars of gold, you know that they are faking it. A person can typically carry about 50 -70 lbs. Each bar weighs about 25 lbs. So a person can carry at most 2-3 of the standard size bars. A cubic foot of gold will weigh more than 1000 lbs.

Talk Like a Physicist

Feb 15, 2008

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How long of a thread do you need to weave a bed sheet?

 TGIF and time for Friday Fermi Problem :

Fermi Problem is described as:

In physics, particularly in physics education, a Fermi problem, Fermi question, or Fermi estimate is an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one’s assumptions. Named for 20th century physicist Enrico Fermi, such problems typically involve making justified guesses about quantities that seem impossible to compute given limited available information.

This is one of the simplest Fermi problems.

Simple Fermi Problem: What is the total length of the thread in a bed sheet?
How long of a thread would you need to weave/make a bedsheet?

No, you may not ask “what is the size of the bedsheet?” – look around, make an educated guess about the average size of a bedsheet.

No, you may not ask “what is the thread count of the bedsheet?” – figure out the most common thread count. If you can not figure it out, you can go to the bedroom and guesstimate the length of the thread in a square inch.


Answer is in the comments. Talk Like a Physicist