https://en.wikipedia.org/wiki/John_Stapp#Work_on_effects_of_... shows that 50 gees is survivable, at which speed you need 120 ms and 3.6 m to decelerate from 60 m/s. Not pleasant but still safer than a car crash. If the airbags inflate before you hit the ground your terminal velocity is much lower, decreasing roughly in inverse proportion to your hydraulic diameter (√(2mg/ρ/A/Cd)), so a 1.5-meter-radius cocoon of airbags around you will cut your terminal velocity to about 20 m/s, at which point you need 40 ms and 400 mm to stop safely. For this you need something like 4-12 1.5-meter-diameter airbags, 7 m² of surface each; at 20-μm thickness that's 140 cc, and if it's mostly something like gel-spun UHMWPE fiber or polyimide film, it's also about 140 g each, so 0.5-1.7 kg total bag weight --- plus conventionally 2 kg of nitrogen per airbag in the form of 3 kg of sodium azide, which is another excellent reason to perform the inflation well before you hit the ground, so you can use atmospheric air instead.
Suppose you weigh 100 kg. To stop you at a safe 20 gees max when you hit, the bag needs to exert 2000 kg max force or 20 kN, so the pressure in a bag acting over something like 1 m² of your body needs to peak at 20 kPa, about 0.2 atmospheres or 2.8 psi. Approximating hoop stress as ½Pr/t we get a bit under 400 MPa stress in the bag, too much for unaided polyimide but an order of magnitude lower than what UHMWPE fiber can handle. So you can make the bag thinner than that, lowering the weight further, perhaps to 40 g per airbag. There are whiplash shock loading problems conventionally handled in automotive airbags by generous safety factors that can be reduced by origami design and judicious addition of thicker compliant material like nylon.
A 30m airbag would need to be 20x thicker and would have 400x as much area, so it would weigh 8000x as much, 320 kg. This would indeed be unwieldy for a backpack.
You can closely approximate constant deceleration by connecting the airbag under you with other, more voluminous airbags on the other side of you, just as a car tire closely approximates constant pressure when traveling over bumps in the road. But it's not necessary; what's necessary is acceptable peak deceleration and, probably, minimal jerk. It's true that constant deceleration is the best case of minimal distance and time for a given peak deceleration, but even linearly increasing deceleration, like from a Hookean spring, only doubles the time needed to stop when holding the peak deceleration constant, thus multiplying the distance by √2.
So, you see, all the materials and mechanisms necessary are already available, though only in the last few decades. There's no technical risk. It's "just" a question of engineering the thing to not kill people all the time when it fails, based on experience with what the deadly failure modes are. It'll require a lot of work and many deaths, but if people put in the work, it will definitely work.
Let me know if I got any of the calculations wrong!
https://en.wikipedia.org/wiki/John_Stapp#Work_on_effects_of_... shows that 50 gees is survivable, at which speed you need 120 ms and 3.6 m to decelerate from 60 m/s. Not pleasant but still safer than a car crash. If the airbags inflate before you hit the ground your terminal velocity is much lower, decreasing roughly in inverse proportion to your hydraulic diameter (√(2mg/ρ/A/Cd)), so a 1.5-meter-radius cocoon of airbags around you will cut your terminal velocity to about 20 m/s, at which point you need 40 ms and 400 mm to stop safely. For this you need something like 4-12 1.5-meter-diameter airbags, 7 m² of surface each; at 20-μm thickness that's 140 cc, and if it's mostly something like gel-spun UHMWPE fiber or polyimide film, it's also about 140 g each, so 0.5-1.7 kg total bag weight --- plus conventionally 2 kg of nitrogen per airbag in the form of 3 kg of sodium azide, which is another excellent reason to perform the inflation well before you hit the ground, so you can use atmospheric air instead.
Suppose you weigh 100 kg. To stop you at a safe 20 gees max when you hit, the bag needs to exert 2000 kg max force or 20 kN, so the pressure in a bag acting over something like 1 m² of your body needs to peak at 20 kPa, about 0.2 atmospheres or 2.8 psi. Approximating hoop stress as ½Pr/t we get a bit under 400 MPa stress in the bag, too much for unaided polyimide but an order of magnitude lower than what UHMWPE fiber can handle. So you can make the bag thinner than that, lowering the weight further, perhaps to 40 g per airbag. There are whiplash shock loading problems conventionally handled in automotive airbags by generous safety factors that can be reduced by origami design and judicious addition of thicker compliant material like nylon.
A 30m airbag would need to be 20x thicker and would have 400x as much area, so it would weigh 8000x as much, 320 kg. This would indeed be unwieldy for a backpack.
You can closely approximate constant deceleration by connecting the airbag under you with other, more voluminous airbags on the other side of you, just as a car tire closely approximates constant pressure when traveling over bumps in the road. But it's not necessary; what's necessary is acceptable peak deceleration and, probably, minimal jerk. It's true that constant deceleration is the best case of minimal distance and time for a given peak deceleration, but even linearly increasing deceleration, like from a Hookean spring, only doubles the time needed to stop when holding the peak deceleration constant, thus multiplying the distance by √2.
So, you see, all the materials and mechanisms necessary are already available, though only in the last few decades. There's no technical risk. It's "just" a question of engineering the thing to not kill people all the time when it fails, based on experience with what the deadly failure modes are. It'll require a lot of work and many deaths, but if people put in the work, it will definitely work.
Let me know if I got any of the calculations wrong!