D&D 3E/3.5 A ropey issue

[Cleon]

I'm just glad I actually found that in the WSG and wasn't misremembering it having those details!​

Well I started D&Ding with 1E and in my youthful gaming life I never invested in any of the sources in your previous post - although I brought (and read!) the Wilderness Survival Guide as soon as it came out and remember not being impressed by it or the Dungeoneer's Survival Guide. We used equipment costs & weights from the 1E Players Handbook throughout that period, even though the switch to 2E had occurred and I'd got a 2E Player's Handbook it didn't see much use.

I've extensively expanded my collection since then and, while the Arms & Equipment Guide and Aurora's Catalogues are in there - somewhere! - I only remember looking through Aurora's and thinking I should "adopt" the idea of Death Cheese (and by extension, cheese made from other monster milks).

Getting back on track, the 2E rope statistics as quoted are all over the place.

For comparison, in the Arms & Equipment Guide, 2E p 116

"Hemp Rope: ...The diameter of a hemp rope can range from 1/4-inch to three inches or more (found primarily on ships). A fifty-foot length of hemp rope weighs nearly 20 pounds and is capable of holding more than 500 pounds of weight. Cost 1 gp."

"Silk Rope: ...A silk rope is less encumbering to work with (its smooth texture is not as rough on the hands), but does not have the ability to hold as much weight as a hemp rope. Usually no more than 200 pounds can be held by the line at once. A silk rope weighs about eight pounds for a 50-foot length. Cost: 10 gp"

Well those weights and costs match the 2E Player's Handbook but the strengths are pathetic.

A decent hemp rope of that heaviness (2.5 feet per pound, which equates to a 28mm hemp rope) should have a breaking load around 12,000 pounds, so even with a more conservative engineer's safety ratio of 1:12 should be safe with a load of 1,000 pounds not 500, while with the more adventurous ratio of 1:6 I've been using should support 2,000 pounds safely.

Hmm… I like the ring of that master 1:6, I hereby dub thee the "adventurer's ratio".

The 2E silk rope is just as strong as the hemp by weight - both support 50 pounds per pound of rope. That's really crummy for silk, being 40% the strength of a decent silk rope of that thickness, but is possible if the rope is made from very low quality silk made from offcuts and broken cocoons (rather than being spun from single threads unwound from a cocoon after the silkworm inside is killed as is the normal practice).

As mentioned before, the main disadvantage of a silk rope is that the fibres are so fine they abrade through very easily, an undesirable quality in a rope.

From Aurora's Whole Realms Guide, p10

"Rope Ladder: ...Our rope ladders are also useful as bridges. We use only 3/4 inch hemp with 2-inch board slats, for loads up to 800 pounds. Our rope ladders are sold in two-foot increments, minimum of 8 feet, maximum of 60 (1 sp/4 ft)."

That load is about right for a hemp rope ladder of that thickness. If a 13/16 inch hemp rope is 1,000 lbs, a 3/4 inch one is 12²/13² as strong, or has a safe load of 144/169 × 1,000 = 852 pounds.

It's the breaking load of a single rope that matters, since uneven weight distribution can put practically all the load on one side of a ladder, straining only the rope on that side.

Isn't it too cheap though? If it's one silver piece per 4 feet a 50 ft. ladder would cost 12½ silvers.

A regular 50 ft. hemp rope costs 10 sp. The rope ladder has to have two ropes (albeit slightly thinner ones) with extra length for the knots to secure the ladder's slats - let's say the two factors cancel each other out, which be 20 sp for the ropes alone.

So the Aurora rope ladder only costs as much as the rope it's made of.

That might sense if it didn't also have wooden slats - those should increase the cost of the whole thing. I'd also think having to manufacture the thing should add a few coppers to the price as well.

Maybe make it 3 or 4 sp per 10-foot length? The regular 2E hemp rope / Aurora slatted rope ladder is 2 sp per 10 feet.

--p 57--
"Ladder: Our ladders are made of sturdy duskwood and come in 2-foot (7 sp), 6-foot (3 gp), 10-foot (5 gp) and 20-foot (10 gp) sizes. For an extra
gp, our 10- and 20-foot sizes can be fitted with hooks, allowing the ladders
to be strung together and hung from a window or roof. Can support 500 lb vertically and 400 lb laid out horizontally."

Considering how much I'm posting about ropes & chains on this thread, it seems prudent not to expand the subject to ladders. It risks branching out to bridges!

--p 73--
"Chain: A fine chain of gold can win a lady’s hand as surely as a broad
chain of iron will bind that of a hobgoblin. We offer chains in all sizes,
from 1/8-inch wide ornamental chains to 4-inch wide anchor chains. The chain prices listed below are for iron chains. Steel costs twice as much and can bear twice the weight. Silver is 20 times the cost, and gold is 200 times more expensive (available only in 1/8 to 1/2 inch sizes).

Chain (per 25 ft)

Dia	Cost	Wt (lb)	Load (lb)*
1/8"	6 sp	6	12
1/4"	2 gp	18	96
1/2"	5 gp	36	970
3/4"	9 gp	98	2,300
1"	17 gp	130	5,000
2"	25 gp	210	12,000
3"	35 gp	400	27,000
4"	60 gp	700	65,000

* Load does not increase with length; rope weight should be subtracted from total load

The 2E Player's Handbook features two kinds of chain: heavy chain (4 gp & 3 lbs. per ft.) and light chain (3 gp and 1 lb. per ft.). There's no information on their strength in that source.

Since the above Aurora table is for 25 ft. lengths, a light chain is 75 gp and 25 pounds and a heavy chain is 100 gp and 75 pounds.

Neither of those weights are in the table and the price is way higher - a 25 gp Aurora chain is 2 inches thick and weighs 210 pounds, not 25!

The table is for iron chains, which I've estimated has "standard stats" of 3 gold and 4 pounds per 10 feet (supports 1,600 lbs.), while a standard steel chain as per the SRD is 30 gold and 2 pounds per 10 feet (supports 2,400 lbs.). That's three times stronger by weight, but it assumes rather good steel - a two times stronger by weight steel chain as per the Aurora Catalogue is perfectly credible.

What is not so credible is the numbers in that table.

Just consider the scaling:

Chain (per 25 ft)

Dia	Cost	Cost÷Dia²	Wt(lb)	Wt÷Dia²	Wt÷cost	Load(lb)	Ld÷Dia²	Ld÷Wt
⅛"	6 sp	38.4	6	384	10	12	768	2
¼"	2 gp	32	18	288	9	96	1536	5.333
½"	5 gp	20	36	144	7.2	970	3880	26.94
¾"	9 gp	16	98	174.2	10.889	2,300	4,088.89	23.47
1"	17 gp	17	130	130	7.65	5,000	5,000	38.46
2"	25 gp	6.25	210	52.5	8.4	12,000	3,000	57.14
3"	35 gp	3.89	400	44.44	11.429	27,000	3,000	67.5
4"	60_gp	3.75	700	43.75	11.666	65,000	4062.5	92.86
	max​	⅛ vs 4		⅛ vs 4	½ vs 4		⅛ vs 1	⅛ vs 4
	ratio​	10.24		8.777	1.620		6.510	46.43

The relationship between the cross-sectional area (which ought to be proportional to diameter squared unless it's oddly shaped) and the chains cost, weight and load-bearing capacities are all over the place, by a factor of 10.24 for cost (3" vs 1/8"), 8.77 for weight (4" vs 1/8") and 6.51 for load-bearing (1" vs 1/8").

At least the cost scales smoothly, with the chain growing cheaper as it gets thicker - which'd make sense since a smaller chain is more labour intensive to make since it has more links per unit length and eventually riveting or welding those links closed will get 'orribly fiddly.

However, the weight per cross-sectional area shouldn't change since iron doesn't become less dense as it thickens! A ratio of 8.77 would turn regular iron (room temperature density 7.874 g/m³) into a material with a density of 0.897. The last time I checked iron does not float on water!

The price per pound is more consistent, with the costliest (4") being only 1.62 times pricier than the cheapest (1/2"). The way it changes is a bit weird, with most chains being about 10 to 12 pounds per gold piece but the 1/2" and 1" chains being about 7. Maybe those chains are the commonest size and so are a bit cheaper? Perhaps they match the "light chain" and "heavy chain" of the 2E PHB, although they are both about two-thirds heavier than those. But then they're also way cheaper, meaning the Player's Handbook chain is likely some kind of steel.

Most of the chains have a somewhat consistent load to cross-sectional area ratio of 3,000 to 5.000 (I'm ignoring the factor PIE would play in the ratio since it's a constant and we're only considering how the load-bearing ability varies with diameter). The chain does get rapidly weaker at diameters under 1/2 inch, suggesting those thicknesses are poorly made - probably due to whoever forging the chain going cheap and not closing the links properly.

The load vs weight ratio is the most variable of all, with a 4" chain having 46 times the ration of the 1/8" chain.

However, they're all way too weak! My homebrew Iron Chain estimate gives a wrought iron chain that would give a 160:1 load vs weight ratio in a 25 ft. length. My estimates of the SRD chain is 480:1, which is a decent match for high grade steel. Those breaking loads should be up to a hundred times higher!

By comparison, according to my estimated breaking loads, 25 foot length of rope would have load vs weight ratios of 200:1 (hempen), 520:1 (silk) and 900:1 (spider's silk). Remember, silk is actually stronger than steel on a pound-per-pound basis, but is a lot less dense than iron so a chain can be stronger if the diameters are the same.

That's all I have time for, I'll comment on the Aurora ropes later.

EDIT: I forgot to comment on the gold and silver chains in Aurora!

The only difference presented is cost - silver chains are twenty times the price, gold chains two hundred times.

Nope!

Firstly, both gold and silver are somewhat weaker than wrought iron. According to Wikipedia and Strukt, the figures are:

Metal	tensile strength	shear strength	yield strength
Wrought iron	234–372 MPa	193–310 MPa	159–221 MPa
Silver	110-360 MPa		55 MPa
Gold	120–220 MPa		205 MPa (hard)

Those numbers can vary considerably depending on the precise composition of the metal. A chain of high-purity silver can approach or overlap the strength of wrought iron - but will be a good deal softer and start yielding at lower loads than the iron chain would. Pure gold is extremely ductile but it's unlikely a chain would be made from it, presumably a gold chain intended for load bearing would be "hard gold" that's up around 220 MPa tensile and 205 MPa yield.

Also, silver and gold are heavy. It'd depend on the alloy in the chain, but pure silver is 10.49 g/cm³, pure gold 19.30 cm³ and wrought iron ~7.7 g/m³, so a silver chain should be around four-thirds as heavy as an iron one (as iron is roughly 3/4 the density of silver), while a gold chain is 2.5 times as heavy (as iron is 2/5 gold's density).

That will also play into the weight / load performance. The previous tensile strengths are based on cross-section not weight, if gold is 250% the density it'd only be 40% the strength on a pound-per-pound basis. However, it'd be even lower than that since it's weaker than wrought iron - at worst it has 220/372 that 40%, or about 24% the strength per pound.

Silver's a bit better.

 

[Stormonu]

I can't even fathom who or how they did research for these values, but one thing to consider is that for your homebrew you are likely working from modern materials that would be greatly superior to methods and materials used in a more historically medieval society. However, access to magic (even folk magic used by D&D smiths) could excuse the use of more modern methods & values.

Hmm...I found this site, Strength of Manila Rope

Looks like the values for rope from Aurora's (and D&D 2E in general) use the "safe load (safety factor 12)" values. I'm going to look around the site to see if it has values for chain possibly somewhere.

 

[Cleon]

I can't even fathom who or how they did research for these values, but one thing to consider is that for your homebrew you are likely working from modern materials that would be greatly superior to methods and materials used in a more historically medieval society. However, access to magic (even folk magic used by D&D smiths) could excuse the use of more modern methods & values.

Hmm...I found this site, Strength of Manila Rope

Looks like the values for rope from Aurora's (and D&D 2E in general) use the "safe load (safety factor 12)" values. I'm going to look around the site to see if it has values for chain possibly somewhere.

If you look through some of my earlier posts you'll see links to some of the sources I found for the figures, one of which was that engineering toolbox page for manila rope you refer to.

I consider the "modern material issue" probably takes place in some cases, such as the Break DC of the SRD chain which indicates it must be made from high grade steel when such a chain in medieval times would more likely be made of wrought iron, plus the links would be riveted rather than welded close as would often be the case in modern chain.

However, silk and hemp a few centuries ago would be no different than it is today so the ropes should have the same strength. Well, unless the silk is made from genetically engineered animals (like goats!) but by the same token, D&D silk ropes could be made from the silk of giant insects and arachnids which might be even more superior.

 

[Cleon]

Let's finish of by considering Aurora's ropes.

--- p 74 ---

ROPE: We offer many varieties of rope, from narrow strings useful for
ornamentation up to massive ropes used aboard ships. All of our ropes utilize the optimum weave, from a triple braid in our string stock to a dual pentad braid.
The widths of hemp rope up to 1 inch are shaved for easier handling.
Hemp Rope (per 50 ft)*

Dia	Cost	Wt lb	Load lb**
1/16"	5 cp	1/3	10
1/4"	2 sp	2	50
1/2"	5 sp	9	225
3/4"	1 gp	20	500
1"	2 gp	36	900
2"	7 gp	142	3,550
3"	16 gp	320	8,000
4"	28 gp	570	14,250

* Multiply width by 10 for rope hp's
** Load does not increase with length; rope weight should be subtracted from total load At times, a smoother, lighter, or stronger rope is needed for a specific task. In these cases, silk is the best choice. Silk rope is easy on the hands and resists twisting and binding. All our silk ropes are woven by elven artisans.
Silk Rope (per 50 ft)*

Dia	50 ft.	Wt lb	Load lb **
1/8"	2 gp	1 1/2	60
1/4"	4 gp	3 1/2	140
1/2"	10 gp	8	320
3/4"	23 gp	18	720
1 "	50 gp	30	1200

* Multiply width by 15 for rope hps
** Load does not increase with length; rope weight should be subtracted from total load

It seems odd that the hempen rope jumps from 1/16 inches to 1/4 rather than starting with a 1/8 line like all the other examples. I'm wondering whether that was an error, since if it were 1/8 inch diameter the rope fits the progression better, as shown in red in the following comparison tables:

Hemp
Dia	Cost(gp)	Cost÷Dia²	Wt(lb)	Wt÷Dia²	Wt÷cost	Load(lb)	Ld÷Dia²	Ld÷Wt
1/16"	0.05	12.8	1/3	85.333	6.666	10	2560	30
1/8"?	5 cp?	3.2?	0.333?	21.333?	6.666?	10	640?	30?
1/4"	0.2	3.2	2	32	10	50	800	25
1/2"	0.5	2	9	36	18	225	900	25
3/4"	1	1.777	20	35.555	20	500	888.89	25
1	2	2	36	36	18	900	900	25
2	7	1.75	142	35.5	20.29	3,550	887.5	25
3	16	1.777	320	35.555	20	8,000	888.89	25
4	28	1.75	570	35.625	20.36	14,250	890.625	25
	max​	1/16 vs 3		1/16.vs.1	1/16.vs.4		1/16vs.¼	1/16.vs.all
	ratio​	1.8286		1.6875	3.0536		1.40625	1.2
Silk
Dia (in)	Cost (gp)	Cost÷Dia²	Wt (lb)	Wt÷Dia²	Wt÷cost	Load (lb)	Ld÷Dia²	Ld÷Wt
1/8"	2	128	1.5	96	0.75	60	3840	40
1/4"	4	64	3.5	56	0.875	140	2240	40
1/2"	10	40	8	32	0.8	320	1280	40
3/4	23	40.889	18	32	0.783	720	1280	40
1	50	50	30	30	0.6	1,200	1200	40
	max​	⅛ vs 1		⅛ vs 1	¼ vs 1		⅛ vs 1	none
	ratio​	3.2		3.2	1.458333		3.2	1

Now what's interesting is the ropes' diameters, weights and loads are rather consistent, not all over the place like Aurora's chains are.

Look at the load-to-weight ratios. Hemp is 25 (except for the anomalous 1.16 inch rope which is 30) and every silk rope is 40. That means an Aurora silk rope is 160% the strength of a hemp rope of the same heaviness, which is lower than the 260% proportion of my estimated 1,300 pound safe load but is not outside the bounds of possibility if the Aurora version is made from weaker silk.

However, the overall strength is about half what it should be even if the authors used a 1:12 safety ratio instead of the 1:6 one I did, since the basic rope is twice as heavy and has half the safe load, it is only one-fourth my estimated strength for a hempen rope.

 

[Cleon]

Might as well finish off the magic item commentary with Pathfinder's enchanted lines.

Three of them are magic weapons:

Net of Snaring (Pathfinder)
Price 28,940 gp; Slot none; CL 11th; Weight 6 lbs.; Aura moderate conjuration and transmutation

DESCRIPTION
This +1 distance net seems lighter than expected and is slightly sticky to the touch.

Three times per day, the wielder may speak the command word and throw the net of snaring at a target. This is a ranged touch attack with a range of 40 feet. The net immediately grows by two size categories. If the attack hits, the target must succeed at a DC 25 Reflex save or become entangled. So long as the wielder retains control of the trailing rope, he may attempt or otherwise act on a grapple as a free action that does not provoke an attack of opportunity. Speaking the command word again shrinks the item to normal size so long as no creature is confined within it.

CONSTRUCTION REQUIREMENTS
Feats Craft Magic Arms and Armor, levitate, permanency, shrink item, web; Cost 14,470 gp; Source Pathfinder Player Companion: Dragonslayer’s Handbook (2013)

The Pathfinder version of the net of snaring is mostly a standard magic weapon apart from its 3 times per day snaring ability. As far as the attributes of its ropes, I see no reason its Break DC would differ from my estimates for the SRD net of snaring.

Vindictive Harpoon (Pathfinder)
Aura moderate transmutation; CL 9th; Slot none; Price 10,305 gp; Weight 16 lbs.

DESCRIPTION
This +1 returning harpoon is made from the jagged, scrimshaw-carved tusk of a narwhal attached to a 50-foot length of woven sinew. Unlike most thrown weapons, a vindictive harpoon functions as well underwater as on land, and its wielder takes no penalties on attack rolls underwater.

CONSTRUCTION REQUIREMENTS
Feats Craft Magic Arms and Armor; Spells freedom of movement, telekinesis; Cost 5,305 gp

My main rope-related question about the vindictive harpoon is what stats does the "50-foot length of woven sinew". I could start rummaging across the internet for the mechanical properties of sinew, but I think I'll keep it simple and say the line is as strong as a +1 hempen rope and leave it at that.

Rope, Razored (Pathfinder)
Aura medium transmutation; CL 3rd; Slot none; Price 8,301 gp; Weight 3 lbs.

DESCRIPTION
A razored rope is a +1 lasso made out of tightly braided lengths of fine chain, used to help restrain cowards attempting to flee a battle. It can be used to entangle an opponent as normal, but deals 1d4 points of damage to a creature that attempts to slip free and fails. The razored rope is also more difficult to escape from, requiring a DC 18 Escape Artist check to slip free from and a DC 28 Strength check to break.

If your patron is a god of battle, as a standard action you can cause the lasso to constrict around a creature already entangled by the rope, dealing 1d4 points of damage.

If your patron is not a god of battle and you attempt to make the lasso constrict, it lashes up and strikes you for 1d4 points of damage.

CONSTRUCTION REQUIREMENTS
Feats Craft Wondrous Item, animate rope; Cost 4,150 gp; Source Pathfinder Player Companion: Faiths of Balance (2011)

The first curiosity about the razored rope is why is made with Craft Wondrous Item rather than Craft Magic Arms or Armor since it is a +1 lasso? Those are weapons you know!

The second point of interest is the description give it Break DC 28, which seems just right. It's made of "fine chain" and regular chain is DC 26, and a +1 weapon enchantment should increase that by +2.

Thirdly, the 3 pound weight is a bit odd - a lasso is normally 5 pounds and magic weapons in 3E aren't normally any lighter unless they're made out of non-standard materials. I guess it could be made out of mithral (which halves the weight) but that would surely be mentioned in the description. Plus it would give it hardness 15 rather than the default hardness of a +1 lasso. I guess the lightness could just be a minor additional feature of its enchantment.

Finally, the cost is a close match to a +2 lasso (which'd cost 2,300 gp 1 sp by Pathfinder RAW). Maybe the writer costed its additional abilities (like being able to do damage, lightness, and higher Escape Artist check DC) are being equivalent to a +1 bonus.

Oh, I thought of another point. The 1d3 points of damage it does is typeless. Shouldn't it be slashing damage. From, like, razors?

 

[Cleon]

Robe of Infinite Twine (Pathfinder)
Aura moderate conjuration; CL 7th; Slot body; Price 1,000 gp; Weight 1 lb.

DESCRIPTION
This coarse hempen robe seems made from a single strand of twine.

The wearer can draw up to 30 feet of twine or up to 10 feet of hemp rope per round from the robe without harming it. As an immediate action, the wearer can draw up to 150 feet of twine or 50 feet of rope from the robe, but this gives the robe the broken condition and suppresses its powers until it is repaired. Twine or rope drawn from the robe remains connected until cut or torn, but is treated as common material rather than part of a magic item. Pieces removed become normal twine or rope.

CONSTRUCTION REQUIREMENTS
Feats Craft Wondrous Item, minor creation; Cost 500 gp; Source Ultimate Equipment (2012)

The only comment I have about this enchanted robe is that it's yet another phenomena that would break the stated economy of the game world.

It can produce 10 feet of hemp rope per round.

That is 100 feet of hemp rope per minute.

Which is 6,000 feet of hemp rope per hour.

That becomes 144,000 feet of hemp rope per day.

And the rope becomes normal, common material if cut or torn of the robe of infinite twine.

So if the proud owner of this magic item hires a bunch of peasants to wear the thing in shifts and just coil rope from it, they can produce the equivalent of 2,880 standard 50-ft ropes every day. Normally you sell new goods for half their value (so 1,440 gp in this case), but I would hope a sensible DM would say they're "flooding the market" which'll drop the price by half or more.

Even quarter-price that's 720 gp a day, or over a quarter of a million gold pieces per year. Not bad for something that costs 1,000 gp. Indeed your ropeworkers would pay for the robe in only 33 hours 20 minutes (plus whatever you paid them) - then you could buy another robe of infinite twine!

Obviously, hempen rope would be near worthless if this magic item was common knowledge.

Solution: change "Pieces removed become normal twine or rope" to "Removed pieces vanish a minute after being separated from the robe and can be dispelled as if they were summoned objects" and the problem of economic ropeocalypse will vanish as well!

It wouldn't hurt to put some maximum limit on how much rope can be pulled from a robe of infinite twine at any one time. Maybe the weight the pulling character can push or drag along the ground (500 pounds or 2,500 feet of rope) or the theoretical ultimate breaking weight of an unknotted hemp rope (which I estimated at 6,000 pounds or 30,000 feet) at which point the rope snaps. That's 5.68 miles of rope, which'd take 5 continuous hours to pull from the robe. Should be enough for most purposes!

 

[Cleon]

Rope of Knots (Pathfinder)
Aura moderate conjuration; CL 9th; Weight —; Slot none; Price 6,000 gp

DESCRIPTION
This rope is 100 feet long and can perform all the functions of a rope of climbing. Furthermore, upon command the rope of knots snakes out and knots itself into a rope structure. The rope can tie itself into any structure which can be created out of 100 feet of rope. Possible structures include (but are not limited to) a sturdy rope bridge up to 25 feet long, a 10-foot-square net or hammock, or a 40-foot-tall rope ladder. The rope takes up to 10 rounds to create a complex structure or half that time to return itself to a simple coil. The rope has hardness 1 and 20 hit points. It repairs damage to itself at a rate of 2 hit points every 10 minutes.

CONSTRUCTION REQUIREMENTS
Feats Craft Wondrous Item, animate rope; Cost 3,000 gp; Source Ultimate Equipment (2012)

Since it "can perform all the functions of a rope of climbing" it seems reasonable to assume it has the same safe load of 3,000 pounds, meaning it would have Break DC 27 according to my estimate.

The rope is apparently weightless, which seems a bit strange. Since a 60-foot rope of climbing weighs 3 pounds I'd expect the 100-foot rope of knots to weigh 5 pounds.

I guess it could have "Weight —" to represent it floating weightlessly all the time but it should still have mass. Being able to float would be necessary for it to tie itself into any structure that can be formed from rope (so it can fly across a ravine to build a rope bridge and so on), but ropes of climbing can do similar feats and they still weigh something.

It seems rather cheap for the features it has, including the ability to self-repair as fast as a rope of entanglement. But you can't use it to murder monsters and steal their stuff (or break the world's economy) so that cheapness isn't unbalancing.

 

[Mannahnin]

Great thread! Really fun deep dive nerding here.

 

[Cleon]

Just noticed something. The Rules for Breaking & Entering have "Rope (1 inch diam.)" on the Object Hardness and Hit Points table. Since the hardness (0), hit points (2) and Break DC (23) match hempen rope presumably that's supposed to be the standard rope thickness.

However, as explained at the beginning of this thread one inch diameter is too thick for a hemp rope weighing 10 pounds per 50 feet. A hemp rope of that thickness should weigh about 15 pounds at that length.

 

[Cleon]

Breaking Good or Scaling of Break DCs and Loads
There were a few additions I planned to add to this thread but got distracted by life and the internet as one does.

Firstly, going back to the original idea of the "Strength/Carrying Capacity" method to determine Break DCs, you can reverse-engineer this to get a rough figure for the Break DC of any object meant to handle a particular load.

Starting with the basics, 3E's Carrying Capacity rules is based on a creature's Strength Score. We've been scaling an object's breaking point to the Max Lift of a creature - if a creature can lift a Max Lift who's weight is equal to or greater than the Safe Load of an object, there's a chance that the object will break. For convenience, we've assumed this Safe Load is one-sixth as much as the Breaking Load.

Since Strength checks are rolled on d20s then obviously the odds of breaking starts at 5% and increases in 5% graduations until it reaches 100%. Therefore, if there's a 5% chance of a creature with Strength X creature breaking a line, a creature with Strength X+38 will have a 100% chance (i.e. a Strength 16 orc has a +3 Strength modifier, so has a 5% chance of making a Break DC 23 roll to snap a hempen rope by rolling a 20; a Strength 54 Titan has a +22 Strength modifier so can hit that DC 23 by rolling a 1). A Strength increase from X to X+38 will increase a creature's maximum load increases a tad over nineteen-fold by the way - if you following the official Strength tables exactly the factor varies from around 19.0 to 19.5 - unless creature X has a Strength under 10, which causes their carrying capacity to switch from a geometric progression to a linear one.

Here's a table showing how Carrying Capacity increases with Strength according to the Rules As Written:

Strength & Carrying Capacity Table

Strength	Heavy Load​	Max Load​	Max Lift​	Mod¹​	Ratio²​
0​	n/a​	n/a​	n/a​	n/a​	n/a​
1​	7-10 lb.​	10 lb.​	20 lb.​	–5​	0.10​
2​	14-20 lb.​	20 lb.​	40 lb.​	–4​	0.20​
3​	21-30 lb.​	30 lb.​	60 lb.​	–4​	0.30​
4​	27-40 lb.​	40 lb.​	80 lb.​	–3​	0.40​
5​	34-50 lb.​	50 lb.​	100 lb.​	–3​	0.50​
6​	41-60 lb.​	60 lb.​	120 lb.​	–2​	0.60​
7​	47-70 lb.​	70 lb.​	140 lb.​	–2​	0.70​
8​	54-80 lb.​	80 lb.​	160 lb.​	–1​	0.80​
9​	61-90 lb.​	90 lb.​	180 lb.​	–1​	0.90​
10​	67-100 lb.​	100 lb.​	200 lb.​	+0​	1.00​
11​	77-115 lb.​	115 lb.​	230 lb.​	+0​	1.15​
12​	87-130 lb.​	130 lb.​	260 lb.​	+1​	1.30​
13​	101-150 lb.​	150 lb.​	300 lb.​	+1​	1.50​
14​	117-175 lb.​	175 lb.​	350 lb.​	+2​	1.75​
15​	134-200 lb.​	200 lb.​	400 lb.​	+2​	2.00​
16​	154-230 lb.​	230 lb.​	460 lb.​	+3​	2.30​
17​	174-260 lb.​	260 lb.​	520 lb.​	+3​	2.60​
18​	201-300 lb.​	300 lb.​	600 lb.​	+4​	3.00​
19​	234-350 lb.​	350 lb.​	700 lb.​	+4​	3.50​
20​	267-400 lb.​	400 lb.​	800 lb.​	+5​	4.00​
21​	307-460 lb.​	460 lb.​	920 lb.​	+5​	4.60​
22​	347-520 lb.​	520 lb.​	1,040 lb.​	+6​	5.20​
23​	401-600 lb.​	600 lb.​	1,200 lb.​	+6​	6.00​
24​	467-700 lb.​	700 lb.​	1,400 lb.​	+7​	7.00​
25​	534-800 lb.​	800 lb.​	1,600 lb.​	+7​	8.00​
26​	614-920 lb.​	920 lb.​	1,840 lb.​	+8​	9.20​
27​	694-1,040 lb.​	1,040 lb.​	2,080 lb.​	+8​	10.4​
28​	801-1,200 lb.​	1,200 lb.​	2,400 lb.​	+9​	12.0​
29​	934-1,400 lb.​	1,400 lb.​	2,800 lb.​	+9​	14.0​
30​	1,067-1,600 lb.​	1,600 lb.​	3,200 lb.​	+10​	16.0​
31​	1,227-1,840 lb.​	1,840 lb.​	3,680 lb.​	+10​	18.4​
32​	1,387-2,080 lb.​	2,080 lb.​	4,160 lb.​	+11​	20.8​
33​	1,601-2,400 lb.​	2,400 lb.​	4,800 lb.​	+11​	24.0​
34​	1,867-2,800 lb.​	2,800 lb.​	5,600 lb.​	+12​	28.0​
35​	2,134-3,200 lb.​	3,200 lb.​	6,400 lb.​	+12​	32.0​
36​	2,454-3,680 lb.​	3,680 lb.​	7,360 lb.​	+13​	36.9​
37​	2,774-4,160 lb.​	4,160 lb.​	8,320 lb.​	+13​	41.6​
38​	3,201-4,800 lb.​	4,800 lb.​	9,600 lb.​	+14​	48.0​
39​	3,734-5,600 lb.​	5,600 lb.​	11,200 lb.​	+14​	56.0​
40​	4,267-6,400 lb.​	6,400 lb.​	12,800 lb.​	+15​	64.0​
41​	4,907-7,360 lb.​	7,360 lb.​	14,720 lb.​	+15​	73.6​
42​	5,547-8,320 lb.​	8,320 lb.​	16,640 lb.​	+16​	83.2​
43​	6,401-9,600 lb.​	9,600 lb.​	19,200 lb.​	+16​	96.0​
44​	7,467-11,200 lb.​	11,200 lb.​	22,400 lb.​	+17​	112​
45​	8,534-12,800 lb.​	12,800 lb.​	25,600 lb.​	+17​	128​
46​	9,814-14,720 lb.​	14,720 lb.​	29,440 lb.​	+18​	147​
47​	11,094-16,640 lb.​	16,640 lb.​	33,280 lb.​	+18​	166​
48​	12,801--19,200 lb.​	19,200 lb.​	38,400 lb.​	+19​	192​
49​	14,934-22,400 lb.​	22,400 lb.​	44,800 lb.​	+19​	224​
50​	17,067-25,600 lb.​	25,600 lb.​	51,200 lb.​	+20​	256​
51​	19,627-29,440 lb.​	29,440 lb.​	58,880 lb.​	+20​	256​
52​	22,187-33,280 lb.​	33,280 lb.​	66,560 lb.​	+21​	333​
53​	25,601-38,400 lb.​	38,400 lb.​	76,800 lb.​	+21​	384​
54​	29,867-44,800 lb.​	44,800 lb.​	89,600 lb.​	+22​	448​
55​	34,134-51,200 lb.​	51,200 lb.​	102,400 lb.​	+22​	512​
56​	39,254-58,880 lb.​	58,880 lb.​	117,760 lb.​	+23​	589​
57​	44,374-66,560 lb.​	66,560 lb.​	133,120 lb.​	+23​	666​
58​	51,201-76,800 lb.​	76,800 lb.​	153,600 lb.​	+24​	768​
59​	59,734-89,600 lb.​	89,600 lb.​	179,200 lb.​	+24​	896​
60​	68,267-102,400 lb.​	102,400 lb.​	204,800 lb.​	+25​	1,024​

1 Mod is the Ability Modifier for a creature with this Strength score.
2 Ratio is the ratio between the Max Load and Max Lift of a creature with this Strength score and a creature with Strength 10.

For Strength values higher than 29, a creature's carrying capacity increases by a factor of four ("×4") every time their Strength score increases by +10. Therefore, a Strength increase of +5 will double ("×2") their maximum carrying capacity. Unfortunately, ability modifiers increase every other integer (a Strength of 14 and 15 both grant a +2 Strength modifier), so a +5 Strength increase represents two-and-a-half points of modifier increase, meaning it'll increase a even Strength score's modifier by +2 (i.e. Str 14+5 => Str 19 and +2 to +4) and an odd Strength score's modifier by +3 (i.e. Str 15+5 => Str 20 and +2 to +5).

Also, note that the max lift for a creature with Strength 60 is pretty close to 100 short tons (204,800 is only 2.4% higher than 200,000 pounds, since two-to-the-power-ten is 1,024).

This means:

1. For every 50 points a creature's Strength increases it can lift a thousand times as much, thus +50 is a thousand times, +100 a million times, +150 a thousand million times, +200 a million million (a long-scale billion or a short-scale trillion, depending on what scaling you prefer, let's call it 10¹² for clarity) and so on.
2. You can convert from pounds to tons by adding +55 points to the Strength. Example: a creature with Strength 12 can max lift 260 pounds => one with Strength 67 can max lift 260 tons.
   Alternatively, you can convert from pounds to tons by adding +50 and dividing the poundage by two. Example: a creature with Strength 26 can max lift 1,840 pounds => one with Strength 76 can max lift 920 tons (half of 1,840).

The following convenient table breaks down these progressions:

Strength​	Heavy Load​	Max Load​	Max Lift​	Mod¹​	Ratio²​
+5​	×2​	×2​	×2​	+2½​	×2​
+10​	×4​	×4​	×4​	+5​	×4​
+15​	×8​	×8​	×8​	+7½​	×8​
+20​	×16​	×16​	×16​	+10​	×16​
+25​	×32​	×32​	×32​	+12½​	×32​
+30​	×64​	×64​	×64​	+15​	×64​
+35​	×128​	×128​	×128​	+17½​	×128​
+40​	×256​	×256​	×256​	+20​	×256​
+45​	×512​	×512​	×512​	+22½​	×512​
+50​	×1,000​	×1,000​	×10e3​	+25​	×10³​
+100​	×1000,000​	×1000,000​	×10e6​	+50​	×10⁶​

1 Mod is the Ability Modifier for a creature with this Strength score.
2 Ratio is the ratio between the Max Load and Max Lift of a creature with this Strength score and a creature with Strength 10.

Incidentally, if you're concerned about the 2.4% rounding between 1,000 and 1,024.

Some high value exponential powers of 2 are:

2³⁰=1,073,741,824	approx. 10⁹	equiv. Str +150​
2⁴⁰=1,099,511,627,776	approx. 10¹²	equiv. Str +200​
2⁵⁰=1,125,899,906,842,624	approx. 10¹⁵	equiv. Str +250​
2⁶⁰=1,152,921,504,606,846,976	approx. 10¹⁸	equiv. Str +300​

The official Carrying Capacity rules exponential scaling dictates that a creature gaining a carrying capacity 10¹⁸ times higher(i.e. a milllion million million) will occur at a Strength increase of +299 rather than +300*.

* My computer's calculator gives a figure of Strength +298.9735285398626113083287486541, but it's a logarithmic calculation subject to floating point errors.

The "tipping point" will occur at about the halfway point (Strength +150).

It's unlikely that creatures with 160+ Strength will be encountered that often in an adventure, but if you want to be a stickler for exactitude just add another +1 to the Strength per +299 increase when calculating creatures with million-fold lifting capacities.

Example: A creature with Strength 417 is equivalent to a Strength 17 creature who's a million million million million times stronger (+400) with an additional Strength +1 from the above "rounding correction". Their max lift is 600 pounds [Strength 18's max lift] multiplied by 10²⁴, which is or 6×10²⁶ pounds 3×10²³ short tons or in longhand three hundred thousand million million million short tons! (aka 300 Zettatons, although Orders of Magnitude are rarely used with short tons).