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As a scenario, let's say that a group of heroes is traveling in a hot air balloon as a proof-of-concept for bandit-proof travel. Some particularly well-armed bandits naturally have taken an issue with this, and are trying to shoot the balloon down with crossbows and/or longbows.

The heroes' hot air balloon is moving along at a pretty good clip, such that the bandits only have time for 1-2 good crossbow volleys, for a total of 8-10 bolts.

Assuming these conditions:

  • Could they shoot down a hot air balloon with crossbows or longbows?

  • How high must our heroes be to survive about 8-10 crossbow shots?

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    $\begingroup$ Hi, and welcome to the Worldbuilding Stack Exchange forum! You're asking several questions here, which is normally not allowed on this site. However, you're new and they seem to be related to each other, so mum's the word. $\endgroup$
    – The Daleks
    May 31 at 22:51
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    $\begingroup$ The answers already state that your balloon is pretty safe. and i agree with them. But, provided your ballon for some reason gets within firing range, while the ballon can tolerate punctures pretty well, it's passengers respond a lot less tolerant to such a treatment. $\endgroup$
    – Burki
    Jun 1 at 9:56
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    $\begingroup$ You should know that there are other fairly serious problems/threats involved with travel by balloon, especially in medieval times. Specifically, 1) bad weather is very dangerous, and 2) you have no real control over where you go, and 3) going too high is a dangerous problem and it can be very difficult to get back down again safely. $\endgroup$ Jun 1 at 16:39
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    $\begingroup$ "How high must our heroes be to survive about 8-10 crossbow shots?" – 8-10 crossbow shots to the balloon, or to their bodies? $\endgroup$ Jun 1 at 19:43
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    $\begingroup$ During WWI the British were irritated to discover that a hail of bullets had absolutely no effect on Zeppelins; the bullet holes were just too small to make a difference. Then they tried bullets coated in phosphorus which ignited the hydrogen lift gas, and that was the end of Zeppelins in warfare. $\endgroup$ Jun 2 at 10:37
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They are safe.

A 1000lb medieval crossbow has an initial velocity of around 150 fps (~45.7m/s). Oddly increasing the poundage of the crossbow does not increase the velocity just the allowable weight of the projectile, the distance traveled by the bowstring and the speed the bow can flex act as limits.

I will use the the formula for firing straight up because it gives the maximum possible height and is pretty simple because stuff cancels out

$$ h_\text{max} = h_\text{initial} + \frac{V_0^2}{(2\times g)} $$

fired straight up with no air resistance, comes out to about 360 feet (110m).

A very low flying hot air balloon flies at over 500 feet (152m) -- legally they cannot fly this low today; during the civil war 500ft was considered flying low, 1000ft (~334 yards/ 305 meters) was more common.

so even if the balloon is flying low, you are more than a 100ft short, If it is flying at a reasonable height the bolt does not even make it half way. And that is firing straight up to get the maximum height, firing at an angle means it gets even less height.

As long as they are flying more than about 360 feet up they are perfectly safe from crossbows.

As a side note longbows actually preform a bit better, they have a slightly higher max velocity, crossbows lets you fire heavier projectiles at similar velocities not faster ones. Longbows can manage 177 fps (54m/s) or around 495 feet (165 yards, 151m) straight up.

So stay around 600 feet/200yards/183m/9chains or roughly a furlong and even the best archer on the planet can't touch them.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Jun 3 at 3:02
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    $\begingroup$ According to this site, museumofflight.org/Exhibits/montgolfier-brothers-balloon, the first manned free flight had an elevation of 3000 feet. If that's accurate then John's numbers are realistic for a balloon prototype with 1700s tech. $\endgroup$
    – Jetpack
    Jun 3 at 3:37
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    $\begingroup$ While a bow can generate faster projectile speeds than a crossbow it is much more difficult to fire an arrow from a powerful bow straight up. Firing an arrow from a war bow requires a lot of muscles working together including much of your back. Being able to point straight upwards without ruining that form seems like it would be much more difficult than shooting one normally. On the other hand shooting a crossbow straight upwards is trivial $\endgroup$
    – Kevin
    Jun 3 at 21:04
  • $\begingroup$ The other good part about firing arrows/bolts straight up is that they come straight down too. Makes arrow reuse easier, but has a slight negative downside of landing with as much velocity as it left with. Not good for the archer. $\endgroup$
    – Criggie
    Jun 4 at 1:44
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Even if the balloon flies low enough that you can actually hit it with a crossbow or longbow (and it is surprisingly difficult to aim at a moving object above your head) you won't do much damage.

First of all at the top end of its trajectory the arrow or bolt won't have much penetrating power left.

And you will mostly be hitting the bottom and sides of the balloon envelope and holes there make hardly any difference to buoyancy.
Remember: hot air rises, so little would escape in downward/sideways direction anyway.
In fact: The envelope already has a wide opening at the bottom for the burner!

You best bet is to aim at the people manning the balloon and hope that they loose control of the burner when they duck for cover in the basket.

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    $\begingroup$ Although, fire arrows/bolts might set the envelope material on fire which might have a significant effect on balloon envelope. Also, flammable liquids that make it to the balloon envelope might drip down to the burner causing flames to spread. $\endgroup$
    – Arluin
    Jun 1 at 15:15
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    $\begingroup$ @Arluin Yes, but fire arrows tend to also have a lot more air resistance than normal arrows so your likelihood of even reaching the target goes down with them. $\endgroup$
    – Nosajimiki
    Jun 2 at 20:57
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They are safe but for another reason than people have given

The balloon will be squishy and will flex went hit by an arrow. Think of poking a plastic bag.

If the arrow or quarrel pierces the bag it will get snagged and fill the hole it just created.

The balloons need to be fire retardant to avoid burning up from the fire keeping them aloft so even flaming arrows or bolts would likely be in effective since the flaming part would go out because (A) the oil or naphtha burns off and (B) the inside of the balloon is hot smoke so already has lower $O_2$ content

Counter strategies by groundlings might be to fire weighed hooked arrows. if enough can be snagged in the balloon, the added weight will force the balloon lower and slower. making it easier to hit.

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    $\begingroup$ I think hot air baloons are already designed to produce more hot air than necessary, and let air out through a hole in the top. The pilot can probably just reduce the hole size, unless it's a really serious, sustained assault. $\endgroup$
    – user7868
    Jun 1 at 8:37
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    $\begingroup$ In a medieval setting and given the balloon is a prototype, i doubt there are many safety precautions in place. Particularly, fire retardants on any cloth are a very long shot, i think. So apart from the height / weapon range problems, i think burning arrows are the only chance to get the balloon down. $\endgroup$
    – Burki
    Jun 1 at 9:52
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    $\begingroup$ @Burki Flaming arrows would probably be ideal - except for the fact that flaming arrows will not fly as far - the weight and added aerodynamic drag of whatever you have burning on the end of the arrow will reduce your range somewhat, particularly an issue when firing in an upward direction. (If you have a high point to stand on, such as a cliff, tower, or maybe even another balloon, you could get considerably more effective range.) $\endgroup$ Jun 1 at 14:03
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    $\begingroup$ @hobbamok but... those blades would just get caught on your bow/send the arrow flying recklessly? Feathers are used for fletching because they can give/not interfere when being shot $\endgroup$
    – TCooper
    Jun 1 at 18:23
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    $\begingroup$ And while a particularly stupid bow-man might be willing to fire one arrow with razor-blades substituting for feathers, they wouldn't want to fire a second one after the blades sliced past their bow-hand on the first shot. $\endgroup$
    – Penguino
    Jun 2 at 1:33
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Of course they can. If it's very dry, anyway...

The archers don't wait for the balloon to arrive. As it appears on the horizon upwind of their chosen hunting ground, they strike! They shoot bolts at the dry grass of the opposite hillside. From powerful incendiaries, flames spread quickly, climbing the bone-dry hillside as the horrified passengers of the Bandit Proof Balloon's maiden voyage watch helplessly. The wind draws them ever forward to the fire, at first with indifference. As flames tower high into the air, cold air is sucked in beneath, creating a windscape of treacherous downdrafts that suck the balloon toward the worst part of the fire. No hot air balloon can remain aloft in a column of superheated air.

Bowing to inevitability, the captain makes an emergency release of air, setting down to pay the ransom rather than chance his fate to the flames.

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    $\begingroup$ This is probably the only way to do it. $\endgroup$
    – Charles
    Jun 2 at 20:22
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    $\begingroup$ This is the sort of tactic you only get to use a few times before you run out of suitable hillsides. Plus once an area is burned it becomes a safe passageway for subsequent flights because it can't be burned again $\endgroup$
    – Kevin
    Jun 3 at 21:15
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    $\begingroup$ He said a hot air balloon. If you want me to stop an army of hot air balloons then I need that army of crossbowmen prepared with razor kites and exploding sky lanterns to help even the odds. I make no promises... $\endgroup$ Jun 4 at 21:24
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Please note, this was done with "seems right" figures. There is actual maths performed elsewhere, including the base of my answer. I am intentionally leaving it here, without editing my "seems right" numbers, both for archival purposes and to not have 3-4 homogeneous answers.


First, the distance

So according to a random page from google a medieval style crossbow had a total range of 380-390 yards.

So shooting up will take some distance out of it, but the bolt is "relatively" light, so lets round it to a nice 350 yards.

Now, could it take down a balloon?

The answer is "that depends". In short you'll want to have it puncture/tear a hole/several holes that leak more hot air/floaty gas than can be replaced.

I should imagine the hole made by a standard crossbow bolt is rather small and the material should be rather durable, both as defence and necessity to prevent "minor wear and tear" type things from causing a critical failure on the balloon.

Your bolts could have a very sensitive mechanism that will cause it expand into some claw like fashion for maximum tear potential upon hitting the fabric/balloon. This will increase weight, and cost, of the bolt so we'll now round the range further down to 300 yards.

Can 8-10 bolts take down a balloon?

Ultimately, it's your story so if you say it can, it can.

However, bolts are rather slow to reload so you're better to have 8-10 people fire once rather than 1 person firing 8-10 times.

With the assumptions above, it definitely seems plausible, presuming they're in range.

TL;DR

8-10 people shooting a specialist bolt should be able to take down a balloon from within 300 yards with a solid degree of plausibility. Their effectiveness is increased the closer they are as it's likely they can punch through both sides of the balloon.

Addressing comments

Hot air balloons fly between 1000 and 3000 feet

According to google, 1000 feet is 333 yards, so that puts the lower bound of flying into the upper bound of "lucky shot".

If this is going to be a hard constant, it turns "plausible" to "highly unlikely".

You mentioned this is a prototype, so I'd wager they'd be rather hesitant to fly too high for fear of coming down hard. That would mean your bandits stand a chance if they stay just above the treetops or lowish over hills/plains.

Can a medieval person find wind currents?

Predictably, maybe not. But it won't take that experienced a pilot to quickly figure out that different heights tend to have winds that blow different directions and act accordingly. This method is used by birds so I'm sure a human can figure it out.

A skilled pilot may be able to predict these with more accuracy. Even if it's "mountains tend to make the balloon want to go direction" rather than a scientific reasoning.


Please note, no maths was actually performed so actual results may vary significantly. I just applied some common sense "fridge logic".

For actual maths, please see John's answer, the result is quoted below:

As long as they are flying more than about ~ 120yards up they are perfectly safe.

As a side note longbows actually preform a bit better, they have a slightly higher max velocity, crossbows lets you fire heavier projectiles at similar velocities not faster ones. Longbows can manage 177 fps or around ~165 yards straight up. So stay around 200 yards and even the best archer on the planet can't touch them.

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    $\begingroup$ Note that with mass-volley fire if the bolts can actually reach the balloon I would think there nearly as much chance of fatally wounding the crew. And hot-air balloons are very mass-sensitive so armor doesn't seem like a particularly feasible response when flying out of reach is so much easier. $\endgroup$ May 31 at 23:26
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    $\begingroup$ how lite the bolt is does not matter, the bolt is not going anywhere near its maximum horizontal distance in the vertical. It will be lucky to make 200 yards. $\endgroup$
    – John
    Jun 1 at 0:36
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    $\begingroup$ @josh it matters for horizontal difference, for maximum vertical the mass cancels out. maximum horizontal distance many times larger than maximum vertical distance. $\endgroup$
    – John
    Jun 1 at 1:09
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    $\begingroup$ If the max range is X, the maximum height is X/2. There is no way for a crossbow with range 390 yards to reach 300 yards when firing vertically. And the mass has no relevance at all in the calculation for range. $\endgroup$
    – L.Dutch
    Jun 1 at 4:30
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    $\begingroup$ A balloon big enough to carry "A party of heroes" could take dozens, possibly hundreds of punctures before the balloon operator notices. The whole operational principle of a hot air balloon even involves the operator periodically opening a large, multi-meter diameter hole at the top to vent hot air, and a few finger-sized holes aren't gonna do jack. $\endgroup$
    – Dragongeek
    Jun 1 at 15:14
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If you compare a medieval archer to a real balloon, the balloon will win. But real balloons were made in the 1780s and your balloon is made in the medieval era.

Your balloon was was created by an inventor who does not have the scientific background, technology, supply chain, or infrastructure that the Montgolfier brothers did. The fact that it can lift a person off the ground at all is an astonishing futuristic marvel centuries ahead of its time. If the balloon can fly so high and so reliably that there is drama about whether archers will threaten its flight, then that is the sort of epic achievement that is worthy of a story.

All in all, a medieval balloon that can carry a person is in the realm of suspension of disbelief. If you want a balloon that can barely lift, or that sinks at the least convenient time, that's at least as believable as a balloon that keeps people successfully out of range.

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Archers can't reach you once you're aloft, but you're far from bandit-proof. Balloons are extremely slow. Average balloon speed is under 10 mph for safe operation (during liftoff and landing you want it as close to zero speed as possible). A horse can trot at 8-12 mph, and gallop close to 30 mph. Your balloon is also quite large and has nowhere to hide while aloft. That means that your bandits won't have much trouble following you (modern balloons typically have a "chase crew" that does exactly this, to give the passengers a ride back to the starting point). You have to land eventually, and the bandits will be right there waiting to shoot you down the moment you get low enough.

The only way to be bandit-proof is if you escape over mountains, a large body of water, or some other impassible terrain. You're at the mercy of the wind, however, so there's no way to know in advance if you'll sail over the impassible mountains or into the very-passable prairie. There's also the inherent danger in being blown towards a mountain (crashing or being swept up higher than your balloon can handle) or out over a sea (stuck with no way back to land).

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