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A ropey issue
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<blockquote data-quote="Cleon" data-source="post: 8144131" data-attributes="member: 57383"><p>Well since I've got this far I might as well do the other item of rigging in the SRD:</p><p></p><p><strong>Chain</strong>: Chain has hardness 10 and 5 hit points. It can be burst with a DC 26 Strength check. (10 ft., 30 gp, 2 lb).</p><p></p><p><strong><span style="font-size: 18px">First Approach</span></strong></p><p>Using the "<strong>Break DCs vs Strength/Carrying Capacity</strong>" method.</p><p></p><p><strong>Chain</strong>: Break DC 26 => safe Strength bonus +15 => Str 40-41 => max lift 6,400 or 7,360 lb. => max load 12,800 or 14,720 lb.</p><p></p><p>Okie-dokey, if we use the natural fibre rope's 1/6th safe load ratio that's a safe working load of 2,100 to 2,500 pounds and a max working load of 6,300 to 7,500 pounds.</p><p></p><p><strong><span style="font-size: 18px">Second Approach</span></strong></p><p>Okay, the big problem is <em>what is this blinking thing made of!</em> It could be anything from pig iron to the best quality steel. Heck, I vaguely remember seeing pictures of a chain made out of wood.</p><p></p><p>The SRD chain is comparatively expensive (3 silver pieces per foot) and as heavy as hempen rope at 5 feet per pound (0.2 lb/ft. or 0.298 kg/m).</p><p></p><p>Come to think of it, the SRD chain costs four times as much per pound as a longsword (30 gp for 2 lb. versus 15 gp for 4 lb.). That suggests it's made from high quality metal at least as good as a typical sword.</p><p></p><p><em><strong>Steel Rope</strong></em></p><p>The closest match on engineering toolbox is <a href="https://www.engineeringtoolbox.com/wire-rope-strength-d_1518.html" target="_blank"><strong>wire rope</strong></a> - that weight lies between 5/16th inch (0.16 lb/ft., min breaking strength 8,520 lb.) and 3/8th inch (0.24 lb/ft., min breaking strength 12,200 lb.) diameters.</p><p></p><p>Averaging out the weight/length and min breaking strength suggests a 0.2 lb/ft. wire rope has a minimum breaking strength around 10,325 pounds, which is a bit lower than the first approach's 12,800 or 14,720 lb. breaking load. However, wire ropes and metal chains have a <a href="https://rlsdhamal.com/safe-working-load-safety-factor/" target="_blank"><strong>better safe load ratio</strong></a> than natural fibre (notice the table uses a 1:4 ratio rather than the 1:12 on the <a href="https://www.engineeringtoolbox.com/manila-rope-strength-d_1512.html" target="_blank"><strong>manila rope</strong></a> and <a href="https://www.engineeringtoolbox.com/sisal-rope-strength-d_1517.html" target="_blank"><strong>sisal rope</strong></a> engineering toolbox pages), so the safe load of a 0.2 lb/ft. wire rope would be around 2,580 pounds - pretty much the safe working load derived from the First Approach, which seems close enough for casual D&D engineering maths.</p><p></p><p>However there's a <em>slight</em> problem - the stats are for wire rope, not a chain!</p><p></p><p><em><strong>Steel Chain</strong></em></p><p>A bit of internet rummaging turned up a <a href="https://www.harken.com/uploadedFiles/Product_Support/PDF/15_ref-breaking-loads_HORIZ.pdf" target="_blank"><strong>typical rigging breaking loads</strong></a> for various types of metal rigging which tells me how strong they are, but unfortunately not how heavy they are.</p><p></p><p>Then I came across <strong><a href="https://setsail.com/chain-size-break-strength-and-safe-working-load/" target="_blank">Chain Size – Break Strength and Safe Working Load</a></strong> on setsail.com which contained some useful factoids, namely:</p><ul> <li data-xf-list-type="ul">3/8″/9.6mm Grade 70 – break strength 24,000 pounds/10,880 kg</li> <li data-xf-list-type="ul">5/8″/16mm Proof Coil – break strength 27,600 pounds/12.500 kg<br /> <br /> Assuming you carry 300 feet/90meters of chain, the 3/8″ will weight in at 408 pounds/185 kg. The 5/8″ weighs 1107 pounds/502kg.</li> </ul><p>The above appear reasonably in agreement to the rigging breaking loads data sheet - the 3/8" stainless rod rigging's breaking load is 22,500 pounds.</p><p></p><p>A 10 ft. length of chain like the SRD version will weigh one-thirtieth the above. So, putting that together:</p><p></p><p>3/8" grade 70 chain, break load 24,000 lb, 10 ft. length weighs 13.6 lb.</p><p>5/8" proof coil chain, break load 27,000 lb, 10 ft. length weighs 36.9 lb.</p><p></p><p>The grade 70 chain is 6.8 times heavier than the SRD chain, so all things being equal it'll be 6.8 times stronger. If we scale down the chain so the weigh becomes 2 pounds for a 10 foot length:</p><p></p><p>breaking strength = 24,000 / 6.8 = 3,529 pounds.</p><p>diameter = 0.375 / square root (6.8) = 0.144 inches (9/64 in. or 3.65 mm).</p><p></p><p>The metal the chain is made from, <a href="http://www.matweb.com/search/datasheet_print.aspx?matguid=9ccee2d0841a404ca504620085056e14" target="_blank"><strong>Grade 70 Carbon Steel</strong></a>, is a typical steel in terms of strength, with an ultimate tensile strength of 70,300-89,900 lb/in² and a yield strength of 37,700 lb/in².</p><p></p><p>With the recommended 1:4 safety ratio, that's a safe load of 882 pounds, which is WAY lower than the First Approach's result of 2,100-2,500 lbs.</p><p></p><p>That said, a safe load of 2,100 to 2,500 pounds is still possible since high quality steels (such as <a href="https://en.wikipedia.org/wiki/Spring_steel" target="_blank"><strong>spring steel</strong></a>) can be much stronger than the typical Grade 70 used above. For example, <a href="https://www.theworldmaterial.com/sae-aisi-5160-high-carbon-spring-steel/" target="_blank"><strong>5160 spring steel</strong></a> has a breaking strength of 1,025 MPa and a yield strength of 650 MPa. Compared to Grade 70's 485-620 MPa breaking strength and 159–221 MPa yield strength that's roughly twice as strong overall, but it yields to loads three to four times heavier without permanent damage. The even mightier <a href="https://en.wikipedia.org/wiki/Eglin_steel" target="_blank"><strong>Eglin steel</strong></a> has breaking strength 1818 MPa and yield strength of 1,547 MPa, so is three times stronger than Grade 70 steel and its yield load is seven to nine times higher!</p><p></p><p><em><strong>Wrought Iron Chain</strong></em></p><p>I also found an applied science for metal workers' page on <a href="https://chestofbooks.com/crafts/metal/Applied-Science-Metal-Workers/292-Strength-Of-Chains.html" target="_blank"><strong>strength of chains</strong></a> that says it's better to make load-bearing chains out from wrought iron, since it's less brittle than carbon steel (so less prone to shatter under the shock of a sudden load) and easier to repair (since it's more amenable to welding).</p><p></p><p>According to Wikipedia, <a href="https://en.wikipedia.org/wiki/Wrought_iron" target="_blank"><strong>wrought iron</strong></a> has an ultimate tensile strength of 34,000-54,000 lb/in² and a yield strength of 23,000-32,000 lb/in².</p><p></p><p>That metal worker's webpage gives this formula for calculating the safe working strength of wrought iron chains:</p><p></p><p>Safe Load (<span style="font-size: 12px">pounds</span>) = Bar Diameter (<span style="font-size: 12px">inches</span>)² × 0.7854 × 40,000 [<span style="font-size: 12px">tensile strength</span>] × 1.63 [<span style="font-size: 12px">chain link factor</span>] × 0.5 [<span style="font-size: 12px">safety ratio</span>]</p><p></p><p>Which boils down to:</p><p></p><p>Safe Load (<span style="font-size: 12px">pounds</span>) = Bar Diameter (<span style="font-size: 12px">inches</span>)² × 25,604.04</p><p></p><p>Which reverses to:</p><p></p><p>Bar Diameter (<span style="font-size: 12px">inches</span>) = square root of [Safe Load (<span style="font-size: 12px">pounds</span>) / 25,604.04]</p><p></p><p>Plugging a 2,200 pounds safe load into the above gives us a bar diameter of 0.29 inches (7.44 mm). So it's 78% as thick than the 0.375 inch diameter grade 70 steel chain above, which'd make it 0.78 × 0.78 = 61% as heavier*, or roughly 8 pounds for a 10-foot length instead of 2 pounds.</p><p></p><p>HOWEVER, note that the above formula uses a 2:1 safety factor rather than the 4:1 of the engineering references I came across. With a 0.25 safety ratio the chain would be twice as heavy or about 16 pounds, giving it a 0.41 inch bar diameter (10.5 mm).</p><p></p><p>*Fortunately all types of iron and steel have a pretty similar density (at least within a few percent) so there's no need to adjust the volume/thickness to account for the different metal.</p><p></p><p><em><strong>Size & Diameter of Chains</strong></em></p><p>Note that a chain's size measures the diameter of the bar used to make the chain, not the chain's overall dimensions. For example, a 1/2" chain would have links at least 1.5 inches across (a half inch for the bar on each side plus a gap in the middle wide enough for adjacent links to fit through). Thus the actual chain might be 1.6-1.75 inches across, or significantly wider if there's a lot of space within the link.</p><p></p><p>Unlike ropes, chains are not measured under tension, since they are forged rather than woven. Their listed diameter is their rest diameter. A two inch diameter Grade 70 steel rod will break when it stretches to around 121% its normal length. However, once it has stretched a certain point (I guesstimate about 110% if the material's Young's modulus is uniform under stress) the rod will have reaches its yield point and will begin to bend and distort at its weakest point(s), permanently damaging the chain.</p><p></p><p>Wrought iron has a very similar "stretchiness" to Grade 70 steel (its Young's Modulus is 193 GPa versus Grade 70's 200 GPa), but being roughly twice as weak (tensile strength 234-372 MPa vs. 485-620 MPa) it will typically break when it stretches by half as much as the steel (say 111%), though its decent yield strength (159–221 MPa vs. 260 MPa) mean it can stretch and recover a respectable amount (I'd guesstimate about 106-108.5%, sat 107.5 on average).</p><p></p><p><strong><em>Notes on Chain Links</em></strong></p><p>The links of a chain are generally made by bending short sections of metal bar in a loop. The cheapest of chains leave it at that, meaning any stress that's enough to unbend one of the links will cause the chain to fail.</p><p></p><p>Alternatively, up to half of a chain's links are cast as solid metal and bar links are made to string them together - this <em>may</em> be a bit cheaper and less labour intensive than bending every link. Being no expert on chain manufacturing I'm unable to say.</p><p></p><p>Proper chain has the ends of each bar link sealed shut. In thick modern chains the links are typically welded.</p><p></p><p>In Ye Olden Days it was a common practice to <em>rivet</em> the ends of each loop together. The rivets will generally be the weakest point of the chain. Riveted links was the standard method of making mail armour (aka chain armour, which is tautologically called chainmail in D&D), with each link looping around several of its neighbours before being riveted close.</p><p></p><p><span style="font-size: 22px"><strong>Conclusion</strong></span></p><p>The SRD chain is made from high-quality steel bars roughly 1/6 inch thick, resulting in a chain about 0.5 inches in diameter. It can support 2,400 pounds safely, or up to 7,200 lbs with an increasing risk of breakage.</p><p></p><p><span style="font-size: 22px"><strong>Addition</strong></span></p><p>The wrought iron chain inspired me to homebrew the following:</p><p></p><p><strong>Chain, Iron</strong>: Made from 3/8" thick wrought iron bars, resulting in a chain about 1.25 inches in diameter. An iron chain has hardness 10 and 10 hit points, it can be burst with a DC 25 Strength check. The chain can support 1,600 pounds safely, or up to 4,800 lbs with an increasing risk of breakage. (10 ft., 3 gp, 4 lb).</p><p></p><p><strong><em>Comparison to Spider's Silk</em></strong></p><p>Spider silk is stronger than high quality steel per unit weight (while steel may have higher tensile strength in terms of MPa it is also roughly six times denser than silk).</p><p></p><p>The standard spider's silk rope is 40% as light as an SRD chain of the same length (4 pounds vs 10 pounds for a 50 foot length), so if it were as heavy as the chain it'd support 250% the load.</p><p></p><p>A spider's silk rope that's 250% heavier than normal should support 4,500 pounds safely, or up to 13,500 lbs with an increasing risk of it breaking. I estimate it has 15 hit points and Break DC 27.</p><p></p><p>The homebrew iron chain is five times heavier than a spider's silk rope (4 pounds vs 20 pounds for a 50 foot length).</p><p></p><p>A spider's silk rope that's 500% heavier than normal should support 9,000 pounds safely, or up to 27,000 lbs with an increasing risk of it breaking. I estimate it has 30 hit points and Break DC 29.</p></blockquote><p></p>
[QUOTE="Cleon, post: 8144131, member: 57383"] Well since I've got this far I might as well do the other item of rigging in the SRD: [B]Chain[/B]: Chain has hardness 10 and 5 hit points. It can be burst with a DC 26 Strength check. (10 ft., 30 gp, 2 lb). [B][SIZE=5]First Approach[/SIZE][/B] Using the "[B]Break DCs vs Strength/Carrying Capacity[/B]" method. [B]Chain[/B]: Break DC 26 => safe Strength bonus +15 => Str 40-41 => max lift 6,400 or 7,360 lb. => max load 12,800 or 14,720 lb. Okie-dokey, if we use the natural fibre rope's 1/6th safe load ratio that's a safe working load of 2,100 to 2,500 pounds and a max working load of 6,300 to 7,500 pounds. [B][SIZE=5]Second Approach[/SIZE][/B] Okay, the big problem is [I]what is this blinking thing made of![/I] It could be anything from pig iron to the best quality steel. Heck, I vaguely remember seeing pictures of a chain made out of wood. The SRD chain is comparatively expensive (3 silver pieces per foot) and as heavy as hempen rope at 5 feet per pound (0.2 lb/ft. or 0.298 kg/m). Come to think of it, the SRD chain costs four times as much per pound as a longsword (30 gp for 2 lb. versus 15 gp for 4 lb.). That suggests it's made from high quality metal at least as good as a typical sword. [I][B]Steel Rope[/B][/I] The closest match on engineering toolbox is [URL='https://www.engineeringtoolbox.com/wire-rope-strength-d_1518.html'][B]wire rope[/B][/URL] - that weight lies between 5/16th inch (0.16 lb/ft., min breaking strength 8,520 lb.) and 3/8th inch (0.24 lb/ft., min breaking strength 12,200 lb.) diameters. Averaging out the weight/length and min breaking strength suggests a 0.2 lb/ft. wire rope has a minimum breaking strength around 10,325 pounds, which is a bit lower than the first approach's 12,800 or 14,720 lb. breaking load. However, wire ropes and metal chains have a [URL='https://rlsdhamal.com/safe-working-load-safety-factor/'][B]better safe load ratio[/B][/URL] than natural fibre (notice the table uses a 1:4 ratio rather than the 1:12 on the [URL='https://www.engineeringtoolbox.com/manila-rope-strength-d_1512.html'][B]manila rope[/B][/URL] and [URL='https://www.engineeringtoolbox.com/sisal-rope-strength-d_1517.html'][B]sisal rope[/B][/URL] engineering toolbox pages), so the safe load of a 0.2 lb/ft. wire rope would be around 2,580 pounds - pretty much the safe working load derived from the First Approach, which seems close enough for casual D&D engineering maths. However there's a [I]slight[/I] problem - the stats are for wire rope, not a chain! [I][B]Steel Chain[/B][/I] A bit of internet rummaging turned up a [URL='https://www.harken.com/uploadedFiles/Product_Support/PDF/15_ref-breaking-loads_HORIZ.pdf'][B]typical rigging breaking loads[/B][/URL] for various types of metal rigging which tells me how strong they are, but unfortunately not how heavy they are. Then I came across [B][URL='https://setsail.com/chain-size-break-strength-and-safe-working-load/']Chain Size – Break Strength and Safe Working Load[/URL][/B] on setsail.com which contained some useful factoids, namely: [LIST] [*]3/8″/9.6mm Grade 70 – break strength 24,000 pounds/10,880 kg [*]5/8″/16mm Proof Coil – break strength 27,600 pounds/12.500 kg Assuming you carry 300 feet/90meters of chain, the 3/8″ will weight in at 408 pounds/185 kg. The 5/8″ weighs 1107 pounds/502kg. [/LIST] The above appear reasonably in agreement to the rigging breaking loads data sheet - the 3/8" stainless rod rigging's breaking load is 22,500 pounds. A 10 ft. length of chain like the SRD version will weigh one-thirtieth the above. So, putting that together: 3/8" grade 70 chain, break load 24,000 lb, 10 ft. length weighs 13.6 lb. 5/8" proof coil chain, break load 27,000 lb, 10 ft. length weighs 36.9 lb. The grade 70 chain is 6.8 times heavier than the SRD chain, so all things being equal it'll be 6.8 times stronger. If we scale down the chain so the weigh becomes 2 pounds for a 10 foot length: breaking strength = 24,000 / 6.8 = 3,529 pounds. diameter = 0.375 / square root (6.8) = 0.144 inches (9/64 in. or 3.65 mm). The metal the chain is made from, [URL='http://www.matweb.com/search/datasheet_print.aspx?matguid=9ccee2d0841a404ca504620085056e14'][B]Grade 70 Carbon Steel[/B][/URL], is a typical steel in terms of strength, with an ultimate tensile strength of 70,300-89,900 lb/in² and a yield strength of 37,700 lb/in². With the recommended 1:4 safety ratio, that's a safe load of 882 pounds, which is WAY lower than the First Approach's result of 2,100-2,500 lbs. That said, a safe load of 2,100 to 2,500 pounds is still possible since high quality steels (such as [URL='https://en.wikipedia.org/wiki/Spring_steel'][B]spring steel[/B][/URL]) can be much stronger than the typical Grade 70 used above. For example, [URL='https://www.theworldmaterial.com/sae-aisi-5160-high-carbon-spring-steel/'][B]5160 spring steel[/B][/URL] has a breaking strength of 1,025 MPa and a yield strength of 650 MPa. Compared to Grade 70's 485-620 MPa breaking strength and 159–221 MPa yield strength that's roughly twice as strong overall, but it yields to loads three to four times heavier without permanent damage. The even mightier [URL='https://en.wikipedia.org/wiki/Eglin_steel'][B]Eglin steel[/B][/URL] has breaking strength 1818 MPa and yield strength of 1,547 MPa, so is three times stronger than Grade 70 steel and its yield load is seven to nine times higher! [I][B]Wrought Iron Chain[/B][/I] I also found an applied science for metal workers' page on [URL='https://chestofbooks.com/crafts/metal/Applied-Science-Metal-Workers/292-Strength-Of-Chains.html'][B]strength of chains[/B][/URL] that says it's better to make load-bearing chains out from wrought iron, since it's less brittle than carbon steel (so less prone to shatter under the shock of a sudden load) and easier to repair (since it's more amenable to welding). According to Wikipedia, [URL='https://en.wikipedia.org/wiki/Wrought_iron'][B]wrought iron[/B][/URL] has an ultimate tensile strength of 34,000-54,000 lb/in² and a yield strength of 23,000-32,000 lb/in². That metal worker's webpage gives this formula for calculating the safe working strength of wrought iron chains: Safe Load ([SIZE=3]pounds[/SIZE]) = Bar Diameter ([SIZE=3]inches[/SIZE])² × 0.7854 × 40,000 [[SIZE=3]tensile strength[/SIZE]] × 1.63 [[SIZE=3]chain link factor[/SIZE]] × 0.5 [[SIZE=3]safety ratio[/SIZE]] Which boils down to: Safe Load ([SIZE=3]pounds[/SIZE]) = Bar Diameter ([SIZE=3]inches[/SIZE])² × 25,604.04 Which reverses to: Bar Diameter ([SIZE=3]inches[/SIZE]) = square root of [Safe Load ([SIZE=3]pounds[/SIZE]) / 25,604.04] Plugging a 2,200 pounds safe load into the above gives us a bar diameter of 0.29 inches (7.44 mm). So it's 78% as thick than the 0.375 inch diameter grade 70 steel chain above, which'd make it 0.78 × 0.78 = 61% as heavier*, or roughly 8 pounds for a 10-foot length instead of 2 pounds. HOWEVER, note that the above formula uses a 2:1 safety factor rather than the 4:1 of the engineering references I came across. With a 0.25 safety ratio the chain would be twice as heavy or about 16 pounds, giving it a 0.41 inch bar diameter (10.5 mm). *Fortunately all types of iron and steel have a pretty similar density (at least within a few percent) so there's no need to adjust the volume/thickness to account for the different metal. [I][B]Size & Diameter of Chains[/B][/I] Note that a chain's size measures the diameter of the bar used to make the chain, not the chain's overall dimensions. For example, a 1/2" chain would have links at least 1.5 inches across (a half inch for the bar on each side plus a gap in the middle wide enough for adjacent links to fit through). Thus the actual chain might be 1.6-1.75 inches across, or significantly wider if there's a lot of space within the link. Unlike ropes, chains are not measured under tension, since they are forged rather than woven. Their listed diameter is their rest diameter. A two inch diameter Grade 70 steel rod will break when it stretches to around 121% its normal length. However, once it has stretched a certain point (I guesstimate about 110% if the material's Young's modulus is uniform under stress) the rod will have reaches its yield point and will begin to bend and distort at its weakest point(s), permanently damaging the chain. Wrought iron has a very similar "stretchiness" to Grade 70 steel (its Young's Modulus is 193 GPa versus Grade 70's 200 GPa), but being roughly twice as weak (tensile strength 234-372 MPa vs. 485-620 MPa) it will typically break when it stretches by half as much as the steel (say 111%), though its decent yield strength (159–221 MPa vs. 260 MPa) mean it can stretch and recover a respectable amount (I'd guesstimate about 106-108.5%, sat 107.5 on average). [B][I]Notes on Chain Links[/I][/B] The links of a chain are generally made by bending short sections of metal bar in a loop. The cheapest of chains leave it at that, meaning any stress that's enough to unbend one of the links will cause the chain to fail. Alternatively, up to half of a chain's links are cast as solid metal and bar links are made to string them together - this [I]may[/I] be a bit cheaper and less labour intensive than bending every link. Being no expert on chain manufacturing I'm unable to say. Proper chain has the ends of each bar link sealed shut. In thick modern chains the links are typically welded. In Ye Olden Days it was a common practice to [I]rivet[/I] the ends of each loop together. The rivets will generally be the weakest point of the chain. Riveted links was the standard method of making mail armour (aka chain armour, which is tautologically called chainmail in D&D), with each link looping around several of its neighbours before being riveted close. [SIZE=6][B]Conclusion[/B][/SIZE] The SRD chain is made from high-quality steel bars roughly 1/6 inch thick, resulting in a chain about 0.5 inches in diameter. It can support 2,400 pounds safely, or up to 7,200 lbs with an increasing risk of breakage. [SIZE=6][B]Addition[/B][/SIZE] The wrought iron chain inspired me to homebrew the following: [B]Chain, Iron[/B]: Made from 3/8" thick wrought iron bars, resulting in a chain about 1.25 inches in diameter. An iron chain has hardness 10 and 10 hit points, it can be burst with a DC 25 Strength check. The chain can support 1,600 pounds safely, or up to 4,800 lbs with an increasing risk of breakage. (10 ft., 3 gp, 4 lb). [B][I]Comparison to Spider's Silk[/I][/B] Spider silk is stronger than high quality steel per unit weight (while steel may have higher tensile strength in terms of MPa it is also roughly six times denser than silk). The standard spider's silk rope is 40% as light as an SRD chain of the same length (4 pounds vs 10 pounds for a 50 foot length), so if it were as heavy as the chain it'd support 250% the load. A spider's silk rope that's 250% heavier than normal should support 4,500 pounds safely, or up to 13,500 lbs with an increasing risk of it breaking. I estimate it has 15 hit points and Break DC 27. The homebrew iron chain is five times heavier than a spider's silk rope (4 pounds vs 20 pounds for a 50 foot length). A spider's silk rope that's 500% heavier than normal should support 9,000 pounds safely, or up to 27,000 lbs with an increasing risk of it breaking. I estimate it has 30 hit points and Break DC 29. [/QUOTE]
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