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Here's a question just for curiosity.

You measure mass on scales. You could measure volume by submerging in a bath with a snorkel system. But how could you measure a living human's surface area without harming.

Ideas so far:

Using software to make a 3D model from images. Effective, but very high-tech.

Wearing a morph suit and rolling in burrs until completely coated, then working out how many were picked up.

Standing naked in a room of known volume for a set amount of time and recording the temperature change in the room. Would rely on knowing that the skin was uniformly at 37 degrees - could you reliably ensure this?

Preferable solutions would be simpler to implement even if a bit approximate.

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    $\begingroup$ Perhaps you could rephrase this not to mention discussion? After all, we don't want questions to be discussed, we want questions to be answered. $\endgroup$
    – David Z
    Commented Feb 6, 2016 at 13:37
  • $\begingroup$ a simple method to get a quick approximation would be to measure one leg at a point of average thickness and treat it as a cylinder, and times it by two. Do the same for the arms. Calculate the surface area of the head as a sphere, and treat the neck as another cylinder. The most tricky would be the torso, which you could perhaps approximate as a cuboid shape. $\endgroup$
    – Amphibio
    Commented Feb 6, 2016 at 13:51
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    $\begingroup$ I'm voting to close this question as off-topic because it is not about physics $\endgroup$
    – John Rennie
    Commented Feb 6, 2016 at 15:13
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    $\begingroup$ @JohnRennie I'm not quite sure what to say - yes it is physics. Applied physics. Measuring properties. More of a fun question than a professional question admittedly, but then it is the weekend. $\endgroup$
    – CJB
    Commented Feb 7, 2016 at 21:28
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    $\begingroup$ there is the Mosteller method ( Simplified calculation of body-surface area. N Engl J Med 1987;317:1098. ) that is not a measure : area in $m^2 = \sqrt {\frac {Height . Weight} {36}}$. For example, a 78 kg body of 1m80 has $2 m^2$ of skin. This helps to check new experimental results $\endgroup$
    – user46925
    Commented Feb 7, 2016 at 22:27

2 Answers 2

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fun question.

(Find a candidate;) take a given volume $V$ of honey (or paint, or anything dense, sticky and safe enough); cover the body with it; measure a mean thickness $h$ of the film around the body (take as many points as needed around the body); measure the volume $V_o$ of honey left in the jar, ($V-V_o$ is the volume used); the approx. surface of the body is $(V-V_o)/h$

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Using a measuring tape, measure the circumference of the person at as many points as you see fit. Try to space your measurements evenly.

The total area is the sum of all the circumferences times the average spacing between them. This will get your quite close to the right answer - certainly better than the "coat the subject in honey" answer which is fraught with experimental uncertainty.

You might separately calculate the area of the head (approximate the head as an ellipsoid, and compute the area. Then subtract the area of the cross section of the neck).

I expect you can get to better than 10% with this method. Clearly a full 3D laser profilometry measurement will do much better, but would be hard to perform with "readily available instruments".

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  • $\begingroup$ Thank you - I suppose you could plot circumferential length as a function of height and then integrate (as trapezia). You'd certainly get a pretty good estimate of all the main features. Fingers and toes would require more effort for higher precision. $\endgroup$
    – CJB
    Commented Feb 8, 2016 at 9:10
  • $\begingroup$ Yes, treat the smaller objects separately for greater accuracy. $\endgroup$
    – Floris
    Commented Feb 8, 2016 at 10:32

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