How Strong does Shardplate make you?

[AltonTS]

I've been trying to get a sense for how strong plate actually is. I'm more thinking of plate worn by a Radiant, rather than the "dead" plate used post recreance. I've been looking, but beyond it making them stronger, and it being better than a pewter-arm, I'm not getting much information.

I'm using "strength" in the most literal sense. How much can they lift? 500lbs? 5 tons? 50 tons? What is the scale here?

I've been trying to create a skybreaker in a TTRPG (Ascendant), but I need to get a feel for exactly how strong the plate will make the character in order to know how many points to spend making the armor. Ascendant is fairly rules intense as it's attempting to be a physics simulator as much as a game, and I need actual ballpark numbers.

[alder24]

7 hours ago, AltonTS said:

I've been trying to get a sense for how strong plate actually is. I'm more thinking of plate worn by a Radiant, rather than the "dead" plate used post recreance. I've been looking, but beyond it making them stronger, and it being better than a pewter-arm, I'm not getting much information.

I'm using "strength" in the most literal sense. How much can they lift? 500lbs? 5 tons? 50 tons? What is the scale here?

I've been trying to create a skybreaker in a TTRPG (Ascendant), but I need to get a feel for exactly how strong the plate will make the character in order to know how many points to spend making the armor. Ascendant is fairly rules intense as it's attempting to be a physics simulator as much as a game, and I need actual ballpark numbers.

I remember it being said that a dead Shardplate grants the strength of 20 men to its wearer, but I can't find the quote now. A living Shardplate should be comparable. Dalinar stopped a Chasmfiend claw and kicked bodies 20 ft into the air so we can clearly conclude that it's a lot.

[Through The Living Grub He/Him]

I'm gonna take a crack at this, but @DrPhysics just in case.

A basic force formula is Force=(mass)(acceleration) and a quick Google search says that the average weight of a fully grown man is about 200lb, and including muscle mass and carapace increases that to about ~275lb. The distance of 20ft isn't our feet as one Rosharon inch is about 0.92 of our inches, giving the kick @alder24 mentioned (I think the horizontal distance was 20tf) a total distance of ~261in. The formula for acceleration is a change in velocity over a change in time (a=^v/^t) time is uncertain, so I don't know how to calculate that, but I would say it would take about two or three seconds, and he moved a total of 21ft, so a change in velocity of ~7ft/s. Converting to metric we get 125kg, 0.71m/s^2, multiplying these we get 89 Newtons. Something about these numbers feels wrong, but I'm not in an actual physics class and could be doing this wrong.

Edited January 31, 2025 by Xiahida

[Duxredux he/him]

You're building a 4th Ideal Skybreaker? I wish I had more to offer, but that's going to be all sorts of complicated when you stack Plate on top of Lashings. Blades change mass when they resize, so it seems likely that Plate does as well, which can change force calculations if your character isn't just lifting an object, but tackling an opponent. Next, if it functions at all like Dead Plate, it also loses power as it gets damaged and runs low on Stormlight, though that would only happen when the Skybreaker is low as well. Add in that lifting strength benchmarks or height of a thrown opponent is with Roshar's reduced gravity and measurement scale, and we have a lot of moving sliders. I couldn't even begin to guess for an Earth comparison without a lot more detail for what numbers Ascendant needs. For example, when you have variable mass Plate, throwing a power assisted kick after falling x meters with y Lashes, which seems like a relatively basic Skybreaker move, my guess could be in the wrong county let alone in the wrong ballpark. My guess will definitely be wrong if the setting has a different gravity than Earth or Roshar and the Lashings adopt the locale. 

[DrPhysics he/him]

On 1/31/2025 at 8:57 AM, Xiahida said:

The distance of 20ft isn't our feet as one Rosharon inch is about 0.92 of our inches, giving the kick @alder24 mentioned (I think the horizontal distance was 20tf) a total distance of ~261in.

I looked up the part of the book, and it is a horizontal distance of 20 ft. And nice work with the Rosharan conversion. That 261 inches works out to be about 6.6 m (which is what I'll use). 

First, we'll need to establish some guesses as to how strong Dalinar is.

From what I could find, an NFL punter produces an average force of 2000 N (Football Physics by Tim Gay) or 450 lbs, and the foot travels about 0.5 m while in contact with the ball. Note: Much of that force comes from leg momentum, so keeping up that average force while kicking something much heavier (like a person) would be quite a bit higher. But, having a longer leg with more mass (thanks, shardplate) will help. 

Another data point would be single-leg extensions (the lift) which advanced lifters would be able to do 200 lbs (900 N) with a single leg. With that one, though, you don't get the momentum advantage. 

Based on those, I think Dalinar should be able to exert an average force of 1000-1500 N during the kick.

Now, we need to figure out what force you need to send someone flying 6.6 m (20 Rosharan feet). @Xiahida ran into a problem where they couldn't eliminate time. We can get rid of it with a little bit of algebra (which I'm not going to recreate here). Thankfully, the person kicked starts and ends on the ground (Dalinar had knocked them over before kicking them), so we get to use the range equation: R=(v^2/g) sin(2*launch angle).

Solving that for v (the launch speed) and taking into account that g on Roshar is 0.7, and estimating the launch angle to be between 30 (common from kicks) and 45 degrees (maximum range), we can find the launch speed: somewhere between 6.7 and 7.2 m/s.

If we assume that the person goes from at rest to that speed while traveling 0.5 m in roughly a straight line (considering the arc of the foot wouldn't significantly change the answer), we can use kinematics to find their acceleration without needing the time: v_f^2 = v_i^2 + 2ad. That gives us an acceleration between 45 m/s/s and 52 m/s/s (or around 5 g's).

Using the 125 kg from the earlier post, we get a force of 5,600 to 6,500 N Using the wiggle room in the force above (1000 -1500 N), we get the kick being 4-7 times stronger than expected, at minimum. (I've tried to err on the low side in these calculations).

 

Other feats, like holding up the chasmfiend's claw probably would be and even bigger multiplier, but we don't have enough data to figure that out. If you can think of other scenes where a shard bearer shows their strength, we might be able to come up with some more limits.

[Green Hoodie Mistborn he/him]

On 2/4/2025 at 10:01 AM, DrPhysics said:

If you can think of other scenes where a shard bearer shows their strength, we might be able to come up with some more limits.

In the race with Elohkar up the rock formation, Dalinar starts with a standing vertical leap of 8 feet. Based on what we're discussing here, I have to assume that it's describing 8 ft from the bottom of his feet back down to the ground, which is about just over 2x more than NBA Max vert referenced in the 2024 Draft Combine (Top was 42", Avg was 35.3", Median was 35.5", and Mode was 32"; 77 people were tested). Their standing verticals were lower ranging between 24"-35". So depending on if you consider Dalinar was running when he leapt or it was a standing leap... regardless, it was >2x Max vert and closer to 3x a standing leap

Quote

He ran to the bottom of the rock formation as Elhokar galloped up behind. Dalinar leaped—Plate-assisted legs propelling him up some eight feet—and grabbed a handhold in the stone.

Sanderson, Brandon. The Way of Kings: Book One of the Stormlight Archive (The Stormlight Archive, 1) (p. 198). Tor Publishing Group. Kindle Edition. 

 

[Duxredux he/him]

On 2/13/2025 at 12:39 AM, Green Hoodie Mistborn said:

In the race with Elohkar up the rock formation, Dalinar starts with a standing vertical leap of 8 feet. Based on what we're discussing here, I have to assume that it's describing 8 ft from the bottom of his feet back down to the ground, which is about just over 2x more than NBA Max vert referenced in the 2024 Draft Combine (Top was 42", Avg was 35.3", Median was 35.5", and Mode was 32"; 77 people were tested). Their standing verticals were lower ranging between 24"-35". So depending on if you consider Dalinar was running when he leapt or it was a standing leap... regardless, it was >2x Max vert and closer to 3x a standing leap

 

Nice, that looks like usable numbers. What this isn't accounting for is the added weight from the Plate which adds a lot of necessary force.

Dead Shardplate suits can weigh over 100 stoneweights, which if this is the translated IRL modern stone, is over 1400 lbs. Add approximately 250 lbs for Dalinar as a tall and powerfully built Alethi.

As noted,the Rosharan inch is 0.92 of a standard inch, and the local gravity is 0.7 Cosmere standard. 

Converting 8 Rosharan feet to metric gives us 8 x 12 x 0.92 x 0.0254 = 2.243 m for the jump height. 748.427 kg for mass, and 6.86 m/s² for local gravity.

Internet says an athlete jumping from a squat takes about 0.2 seconds.

Kinematics for that would be... vf² = vi ²+ 2ad. 0 = vi² - (2*6.86*2.243), vi = 5.55 m/s I think.

a = v/t = 5.55/0.2 = 27.75 m/s²

F=ma would be F =(748.43*27.75) = about 20,768 newtons, but that's just the force for the jump, not including overcoming gravity. For that, we would add (748.43*6.86), or 5,134 newtons.

So... my ballpark is 25,900 newtons of force on average for Dalinar's 8 foot vertical jump. Does that check out? I expect it to be a tremendous amount of force for something as heavy as a suit of Shardplate to jump that high. 

[DrPhysics he/him]

4 hours ago, Duxredux said:

Kinematics for that would be... vf² = vi ²+ 2ad. 0 = vi² - (2*6.86*2.243), vi = 5.55 m/s I think.

You can leave out time if you set up that equation twice. If 0 is crouch, 1 is leaving the ground, and 2 is at the height of the jump, you get:

v1² = v0 ²+ 2aj*d = 0 + 2aj*d

v2² = v1 ²- 2gh -> 0= v1 ²- 2gh -> v1 ²=2gh

Where d is the crouch distance, aj is the average jump acceleration, and h is the height of the jump. We can skip finding the speed at which the jumper leaves the ground, and just set both v1 ² equal to each other:

2 aj *d = 2gh -> aj = gh/d

Since F=ma and we just want a multiplicative power (e.g. 10x stronger), we  can do a simple:

P = a_armor/a_no_armor = gh_armor/(gh_no_armor)

This assumes that the average crouch doesn't significantly change.

 @Green Hoodie Mistborn gave us jump averages for NBA players (about 90 cm), and I was able to find average population jump averages (60-70 cm for trained males). I'd estimate that Dalinar would be at the upper end of average, but probably not above average for NBA (Notice I left g in the above equation, that lets us scale earth averages to Roshar averages).

So, at the high end:

P = 6.86 * 2.243 / (9.81 * 0.6 ) = 2.6 times stronger

And at the low end:

P = 6.86 * 2.243 / (9.81 * 0.9 ) = 1.75 times stronger

This does ignore the weight of the armor, but when doing leverage calculations like this we usually compare just input and output. If you want to include the armor mass, you can plug it in here:

P =m_tot* a_armor/(m_person*a_no_armor) = m_tot*g*h_armor/(m_person*g*h_no_armor)

The hard part is figuring out how much shardplate weighs.

The book tells us that it can be "over 100 stoneweight", which if you use the modern definition of a stone would be 630 kg. However, that doesn't match what we see in-story.

We know that a regular horse (specially bred for the purpose) can carry someone in a full suit for an extended period. Our largest draft horses can carry about 500 lbs, which scaled to roshar gravity would be a mass of 320 kg. A very muscular man over six feet tall (Dalinar), would come in at 100-110 kg. So for round numbers, a full suit of shard would have a mass of about 200 kg.

We also know that unpowered plate is practically impossible to move in, but no one is injured from the weight of the armor when part of it goes out, which also puts us closer to 200 kg. 

Also, Kaladin is able to pick up and wield a helmet. A helmet is about 14% of the total weight of a regular suit of armor (full armor was 17-25 kg, with the helmet coming in at 2.5-3.5 kg). Assuming that relationship holds true, At 630 kg, the helmet would be 88 kg (comparable to a 135 lb/62 kg weight on earth) whereas at 200 kg, the helmet is 28 kg (43 lb/20 kg on earth). At 200 kg, it is doable with Stormlight (though I'd probably put the armor at 100-150 kg). Kaladin would never be able to wield the helmet from 630 kg armor.

So depending on whether you use 200 kg armor (m_tot/m_person = (100 kg + 200 kg)/100 kg = 3) or 100 kg armor ((100 kg + 100 kg)/100 kg = 2), you'd multiply the force factor by 2-3, giving a range of roughly 4-8 times as much force, which is about the same range as above.

I doubt Brandon or his team actually did this much math for the story, but it's fun to see the two different situations give roughly the same force range.