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One of the first things noted about pretty much any humanoid race with horns or antlers is that the neck would not be able to support the weight, making the idea unfeasible. However, some horns are larger than others, and I find it difficult to believe the idea of horned humanoids is entirely not plausible—especially when taking into account that cutaneous horns are a thing. Ignoring how these horns came to be or what their purpose might be, how large could horns resembling animal horns be on an average human without any charges to the current body plans and muscle structure?

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Depending on the horn design, pretty large:

enter image description here

Size and weight aren't the same thing.

The size will depend on your design and material (and desire to be able to walk through doors) but it looks like you've got around 85kg1 to work with.

enter image description here World's Largest, Heaviest Turban (187-Pounds)

Wonder if this counts as wearing a helmet. Ride safe out there.

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    $\begingroup$ Keep in mind that shape matters too. The larger your horns are for the same weight, the more torque is applied to the head. $\endgroup$ – Pasqueflower Feb 10 '18 at 5:46
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    $\begingroup$ What Pasqueflower said, but keep in mind that length may play a larger role than actual volume when it comes to torque. $\endgroup$ – Renan Feb 10 '18 at 6:18
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    $\begingroup$ Also position. Horns that extend forward are going to far worse for you than vertical horns with a center of mass directly above you. $\endgroup$ – Arcanist Lupus Feb 10 '18 at 7:02
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    $\begingroup$ The concept I believe you're all dancing around is balance. Yes a design without good balance is not making it anywhere close to 187 pounds. $\endgroup$ – candied_orange Feb 10 '18 at 7:46
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Consider that the weight of the horns is utterly trivial compared to the increased danger of snapping the neck with a twisting motion that comes with attaching what are essentially handle bars to the skull. Without modifications to the neck musculature or structure, I would estimate horns could be no more than a few centimetres (and therefore quite light) before they become a liability for people who have them.

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This depends on how dense do they are. If it is a density of a polystyrene foam with very thin hard covering, then horns on the usual "mythological" size like this are not a problem; could probably even be larger.

A cone with 10 cm radius at the base and 50 cm height should weight only about 200 g if made from a polystyrene foam. It would already look like a really large horn.

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