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Explain xkcd: It's 'cause you're dumb.
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We have an explanation for all 2 xkcd comics, and only 42 (2%) are incomplete. Help us finish them!

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6-Foot Zone
Technically now it's a 34-foot zone.
Title text: Technically now it's a 34-foot zone.

Explanation

Ambox notice.png This explanation may be incomplete or incorrect: Created by the 8 social-distancing horses, who are not themselves socially distancing. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.

This comic is the 11th comic of the last 12 (2283: Exa-Exabyte was unrelated) in a series of comics related to the 2020 pandemic of the coronavirus - SARS-CoV-2.

This comic is about social distancing, a common practice to prevent the spread of the COVID-19 disease. It has been suggested to maintain 6 feet (i.e. 1.83 m - in e.g. France and Britain the suggested distance is 2 m) of distance between yourself and other people, to prevent the transmission of respiratory droplets from you to others (or vice versa).

Randall takes this 6 feet of distance, and does calculations of the "area" of distancing, "border", population density, and "real estate value". He finally culminates in determining the number of horses that could also fit in the space.

Randall's border length and approximate area calculations are based on a zone with an outside radius of approximately 6.8 feet or 82 inches (2.07 m), meaning that the person has a radius of approximately 0.8 feet (9.6 in, 0.24 m). That is, 2π(6.8ft) = 42.7 ft and π-1(6.8ft)-2 = 145 ft2.

There are two different population densities that can be calculated. The one used by Randall in the comic is the population density of the exclusion zone itself, i.e. just the reciprocal of its area. This is π-1(6.8 ft)-2 = 190,000 mi-2. A different density is the density of a crowd in which everyone obeys the distancing rules. That would result in 0.9069(π-1)(3.8ft)-2 = 560,000 mi-2 population density. When people stand 6ft apart from each other, their exclusion zones are overlapping; instead we can use smaller circles with 3.8 ft radius that are not overlapping. 0.9069 is the packing density of circles in the plane. For comparison, only 21 countries have a population density >1000 mi-2, but there are a few cities with a population density on the same order of magnitude (~100,000 mi-2).

The USFS Equestrian Design Guidebook is a real thing.

The title text is a pun using the alternate definition of foot, noting that a human has two feet and a horse has four, so 8 × 4 + 2 = 34 feet.

Transcript

Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.
Guide to the 6 foot Social Distancing Zone
Profile image of person with 6 foot distance measurements on both sides
Overhead image of person within a roughly circular shape extending 6 feet in all directions from the person. The dimensions of the person account for the non-circular shape.
Approximate area: 145 square feet
Border length: 43 feet
Population density: 190,000 people/square mile
Value at NYC real estate price per square foot: $195,000
Maximum number of horses that could fit inside it with you, estimated using the dimensions in the US Forest Service Equestrian Design Handbook: 8

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