Strength Modification

[Todjaeger]

I agree with all of this except the first sentence.  All other things being equal, the material that is denser will fall faster (same drag, greater mass and therefore gravitational force, therefore greater terminal velocity).  In addition, how rough the surface of the object is will affect drag.

As an example, consider a 2-inch sphere made of balsa wood, and a 2-inch sphere made of lead.  Same size, same shape, but the lead sphere will not only have a greater gravitational force acting on it, but also a bit less drag, despite having the same shape.  Material does matter.  It's just not the only factor.

The material itself doesn't make a difference, it is the properties of the material as both of us have observed.  Whether that material is a tungsten, lead, uranium or gold-alloy, if the mass relative to surface area is that same, the object will have the same terminal velocity.  Also the gravitional force acting on a falling object on Earth will always be the same, since the relative gravitational force exerted by the Earth's mass doesn't change, hence the acceleration due to gravity being a constant of ~32 ft/sec sq. or ~9.8 m/sec sq.

Also please note I'm not using the term density, but mass relative to surface area.  A dense metal like tungsten, lead, uranium or gold like I previously mentioned will, depending on how the object is space, occupy a significantly less volume of space than an object made of balsa pine which has the same mass.  However, if one were to take a 1 kg mass of lead and arrange it into a single sheet covering a large area, assuming that the lead sheet doesn't tear, it would have a lower terminal velocity than a 1 kg mass of balsa pine in a single block, assuming that that surface area of the lead sheet is greater than that of the block of balsa pine.  Generally speaking, denser materials are going to have a higher mass to surface area ratio than less dense materials, and will therefore have higher terminal velocities since the area of the object will be (usually) less and therefore less subject to drag.  It is not true in all cases though.

-Cheers

[Belial666]

I said "tungsten terminal velocity (for a man-shaped piece)". I.e. take some tungsten and make a statue out of it - I wanted to use existing numbers for humans to make a quick calculation, not recalculate for a tungsten arrow. Since it has a density 20 times that of an actual human (and thus 20 times the weight), the statue tops out at 4,47 times the terminal velocity. Given that a human diving head-first tops at about 300 mph, we get a bit over 1300 mph for the tungsten statue. Now streamline the same material into an arrow that has about 1/6 the projected area for its mass that a human would have. That's another 2,5x increase in terminal velocity. We are now looking at roughly 3250 mph terminal velocity, or close to a mile a second. Of course, said object is not going to actually reach that speed unless you drop it from about 100 miles up.

Now, to impart the same kinetic energy on an arrow weighing 5 pounds, you need 2.600.000 joules. For comparison purposes, the muzzle energy of a .50 BMG round fired from typical HMGs is 15.000 joules, the muzzle energy of an AK-47 round is 2.000 joules and a typical medieval arrow has about 1500 joules kinetic energy when fired.

Giving such kinetic energy however is difficult. You'd need a bow with a draw weight of 75 tons to manage 2/3 of it. If you are a giant and get a big metal bow made out of a huge laminated spring, you can reach those draw weights. For human-sized nonmagical bows the numbers are problematic. The typical laminated spring used in car suspensions could provide only about 2,5 tons of draw weight in a bow that is still sized for humans. You'd need considerably more advanced materials than steel and a good bit of engineering to get to the needed 75 tons. This doesn't mean it's impossible. It just means the bow would be a really, really expensive custom work and it would only work for someone of your mythic strength. You could not hand it off to someone else and hope they can use it - even guys with supernatural strength could not hope to draw it.


OTOH, it should be fairly simple to give vampires or other strong non-people powerful bows. 2,5 tons of draw weight is right in the alley of inhuman strength so go make some bows out of laminated metal springs and give them thin steel arrows.