explain xkcd - User contributions [en]

Talk:3015: D&D Combinatorics

2024-11-23T06:09:21Z

172.69.65.224: add my 2 cents

The bot originally created this page as “D Combinatorics”. I renamed it to the correct title and tried to get as many of the references as possible (including a few redirects). [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 00:54, 23 November 2024 (UTC)

:The title in the Atom feed (which I'm assuming the bot consumes) is "D Combinatorics". I'm guessing something in Randall's pipeline didn't like the ampersand. --[[Special:Contributions/162.158.154.160|162.158.154.160]] 01:41, 23 November 2024 (UTC)

::Yup, if you look at [https://xkcd.com/3015/info.0.json 3015's JSON] you see that <code>title</code> and <code>safe_title</code> differ, and if you look at the HTML page source you'll see '''3''' different things: <code><title>xkcd: D Combinatorics</title></code>, <code><meta property="og:title" content="D&amp;D Combinatorics"></code>, and <code><div id="ctitle">D&D Combinatorics</div></code>! So probably what happened is Randall entered D&D but was supposed to enter D&amp;D, and the openGraph tags adder code, having to be HTML-aware, decoded & normalized D&D as HTML would, but the other parts of the pipeline just ate it for some reason.

:By raw combinatorics: 71 + 52 + 34 + 20 + 10 + 4 + 1 ways to get each of 16 - 22 respectively, for a total of 192, out of 4(6^3) = 864 total. 192/864 simplifies to exactly 2/9. I have no idea how Randall found this; if anyone has an idea, please let me know. [[User:Kaisheng21|Kaisheng21]] ([[User talk:Kaisheng21|talk]]) 01:33, 23 November 2024 (UTC)

It seems like we edited the transcript at the same time. The odds of rolling 16 or higher in this situation seem to be 2/9? [[User:Darkmatterisntsquirrels|Darkmatterisntsquirrels]] ([[User talk:Darkmatterisntsquirrels|talk]]) 01:29, 23 November 2024 (UTC)

: There are 864 possible rolls (6 * 6 * 6 * 4). If you enumerate all of the rolls you will find that 192 are 16 or higher. 192/864 = 2/9, the value from the explanation. [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)

A much simpler approach: Roll two six sided dice and sum the result. You are successful if the result is 5 or 9. That happens 8 times out of 36. 8/36 = 2/9. (Or successful if the sum is 4 or 6, or 2 or 7, or 2,3,4 or 11, or several other combinations.) [[Special:Contributions/172.68.54.139|172.68.54.139]] 01:41, 23 November 2024 (UTC)
:Clever, but dice rolls in D&D involving summing all the dice, applying modifiers, if any, and then comparing to one or more threshold values. Your method makes it very difficult to apply modifiers. [[Special:Contributions/162.158.41.8|162.158.41.8]] 02:49, 23 November 2024 (UTC)

Minor quibble, arrows aren't fired (unless they're flaming or self-propelled, perhaps), they are shot. (Shotguns are fired of course.) [[Special:Contributions/162.158.41.73|162.158.41.73]] 02:52, 23 November 2024 (UTC)

Rolling 22 or lower on percentile dice (or, equivalently, 79 or higher) is close enough, and easier to come up with. (Give or take whether 00 is treated as 100 or zero.) Or directly represent the action: roll a d10. If it's 1-5, you lose. If it's 6-10, roll again; if it's 1-5 you lose, 6-9 you win, 10 roll again. (Modify slightly if you want to distinguish the case of grabbing *two* cursed arrows.) [[User:Jordan Brown|Jordan Brown]] ([[User talk:Jordan Brown|talk]]) 03:26, 23 November 2024 (UTC)

== Alternative exact solution for getting this probability using dice ==

Roll: 1d8, 2d6, 1d4 succeed on 19 or higher.

== Alternative way to calculate the probability of drawing two non-cursed arrows ==

I couldn’t remember the formula for binomial coefficients (“n choose k”), but there’s an easy way to calculate that the probability of drawing no cursed arrows is 2/9 without that formula. You just need to multiply the probabilities that each of the arrows drawn is not cursed. Since only two arrows are drawn, you only have to multiply two numbers.

The probability that the first arrow is not cursed is 5/10 – there are 5 non-cursed arrows and 5 cursed arrows out of 10 total. After taking out one non-cursed arrow, there are 4 non-cursed arrows and 5 cursed arrows out of 9 total, so the probability that the second arrow is not cursed is 4/9. Multiplying the two probabilities, the probability of drawing two non-cursed arrows is (4*5)/(10*9) = 20/90 = 2/9.

I was considering writing this observation in the Explanation section of the page, but I’m not if it belongs there. This solution avoids using formulas from combinatorics, so it might not be connected enough to the comic.—[[User:Roryokane|Roryokane]] ([[User talk:Roryokane|talk]]) 06:02, 23 November 2024 (UTC)

3013: Kedging Cannon

2024-11-20T00:37:03Z

172.69.65.224: /* Explanation */

{{comic
| number = 3013
| date = November 18, 2024
| title = Kedging Cannon
| image = kedging_cannon_2x.png
| imagesize = 740x259px
| noexpand = true
| titletext = The real key was inventing the windmill-powered winch.
}}

==Explanation==
{{incomplete|Created by a HEADCANNON. Do NOT delete this tag too soon.}}

Prior to the invention of powered ships, oceangoing vessels moved primarily by means of wind power, which meant that they were restricted by the direction and power of the winds. If a sailing vessel needs travel upwind, they typically make use of a technique called {{w|Tacking_(sailing)|tacking}} (or "tacking against the wind") which involves zigzagging across the wind's direction. This method is significantly slower and more difficult than traveling downwind, but it makes upwind navigation possible.

This comic portrays a fictional scenario where a ship's captain, apparently unfamiliar with tacking, has developed an alternative method based on {{w|kedging}} (also known as warping).

The basics of kedging are not dissimilar to the comic: a boat affixes a rope or chain to an anchor point (such as a literal anchor) and winches itself closer. Traditional kedging involves deploying an anchor from the vessel, either manually or via a smaller boat, and then {{w|winch|winching}} the ship toward the anchor point using ropes or chains. This is a real method, but is clearly very slow and labor intensive. Generally kedging is only effective in shallow waters and employed when tacking is not an option. The captain in this strip appears to be using it for long-distance travel, which would be highly impractical. What's more, he deploys his anchor with a cannon, wasting large amount of gunpowder, all while a confused Cueball looks on wondering why the Captain isn't trying to use tacking instead.

This approach to transportation has been used in war when the wind halts, with ongoing gunfire. This may be where the concept of using a cannon to send the anchor came from, as such a situation may involve an excess supply of gunpowder.

Where the water is too deep for the anchor to reach the bottom, a so-called {{w|sea anchor}} could theoretically be used, but would be even less practical. Kedging with a sea anchor would effectively be a very slow and inefficient version of rowing, which is alternative (albeit labor-intensive) method to travel against the wind.

The title text indicates that the captain's system has evolved to incorporate a windmill mechanism that harnesses wind power to draw in the kedging rope. Windmills are much more intuitive to use for kinetic energy, as the concepts behind the airfoil are very commonly misunderstood as mentioned in a past comic of Randals involving common misbeliefs. The comment brings to mind the comparison of the energy efficiency of a windmill closing a rope vs normal tacking, which different audiences will have different intuitions about, and as such the joke will land differently for different people, but likely this is a ridiculously inefficient rube-goldberg-like solution to wind propulsion, in the context of tacking being discovered, and an ingenious energy saver (if heavy and expensive) in the context of it not. An analysis of the efficiency is below.

{{cot|Speed and economic analysis of dual wind-winched kedging cannons compared to tacking}}
A dual-anchor kedging cannon system for sailing upwind, consisting of:
* Two kedging cannons firing 16 kg anchors
* 6-meter diameter windmill powering winch system
* Dual-winch setup for continuous operation
* Operating in 15 knot headwind conditions

Vessel specifications:
* Length: 30 feet (9.1 meters)
* Displacement: 10,000 lbs (4536 kg)
* Sail area: 600 sq ft (55.7 m²)
* Wetted surface: 40 m²
* Frontal area: 8 m²

;Wind power generation
Available wind power is given by:
''P'' = ½''ρAv''³''η''
where:
* ''ρ'' = 1.225 kg/m³ (air density)
* ''A'' = ''π''(''D''/2)² = 28.3 m² (windmill area)
* ''v'' = 7.72 m/s (wind speed)
* ''η'' = 0.245 (combined efficiency)

This yields 1.95 kW of usable power.

;Drag forces
Total drag combines water and air resistance:
''F''drag = ''F''water + ''F''wind
where:
* ''F''water = ½''ρ''w''C''d''A''w''v''²
* ''F''wind = ½''ρ''a''C''a''A''f''v''²

Using:
* Water density (''ρ''w) = 1025 kg/m³
* Hull drag coefficient (''C''d) = 0.04
* Wetted area (''A''w) = 40 m²
* Air density (''ρ''a) = 1.225 kg/m³
* Air drag coefficient (''C''a) = 0.8
* Frontal area (''A''f) = 8 m²

Total drag force = 1053.4 N

;Anchor ballistics
For 300 m range with 45° launch angle:
* Required velocity = 54.7 m/s
* Launch energy = 23.7 kJ
* Black powder energy per shot = 680.4 kJ
* Launch efficiency = 3.5%

;System performance
* Winch speed = 3.60 knots
* Cycle time = 194.7 seconds
* Effective speed = 3.04 knots
* Compared to tacking speed = 4.95 knots
* Speed ratio (kedging/tacking) = 0.61

;Economic analysis
* Shots needed per nautical mile: 6.1
* Black powder cost per shot: $10 (0.5 lbs @ $20/lb)
* Cost per nautical mile: $60.76
* Powder consumption: 9.2 lbs/hour
* Operating cost: $184.90/hour

Example 100 nmi journey:
* Total powder cost: $6,076.12
* Journey time: 32.9 hours

;Conclusion
The dual-anchor kedging cannon system is both slower and significantly more expensive than traditional tacking:

Speed disadvantage:
* Achieves only 61% of tacking speed
* 100 nmi journey takes 32.9 hours vs 20.2 hours tacking

Economic disadvantage:
* High powder costs ($60.76 per nautical mile)
* Requires significant powder storage (303 lbs for 100 nmi journey)
* Additional wear and tear on mechanical systems

Key limiting factors:
* Limited wind power available (1.95 kW from 6 m windmill)
* High drag forces (1053.4 N total)
* Poor ballistic efficiency (3.5% of powder energy converts to useful launch)
* Long cycle times due to realistic winching speeds

The system could potentially be improved by:
* Larger windmill (though practical size limits on boats)
* More aerodynamic anchor design
* More efficient powder-to-launch energy conversion
* Reduced transfer time between anchors

Therefore, given both the energy constraints and economic factors, traditional tacking remains far more practical for upwind progress. The key insight is that while the kedging cannon seems to "cheat" the wind by going straight upwind, it actually requires converting wind energy to mechanical work less efficiently than a well-designed sail plan, while also consuming expensive gunpowder. The indirect path of tacking makes better use of the available wind force with no consumable costs.
{{cob}}

==Transcript==
:[A two-masted sailing ship with its sails up is floating on a calm sea with tiny waves. Two tiny figures can be seen at the ship's bow. One of them is speaking. In the next panel it becomes clear this is the captain.]
:Captain: I hope someday someone invents a way to sail upwind.
:Captain: Using the kedging cannon just wastes so much gunpowder.

:[Close-up on the deck of the ship, showing two persons behind the taffrail. Cueball is standing behind the ship's captain and talking to him. The captain is wearing a black bicorne navy hat and aiming a cannon containing an anchor forward. Chains are draped from the cannon.]
:Cueball: The '''''what?'''''
:Cueball: Wait, do you not know how to sail upwind? Is that why your ship takes forever to--
:Captain: Stand by...'''''Fire!'''''

:[Distant shot showing the anchor and its chain being launched out in front of the ship, towards the right of the panel. Cueball and the Captain can still be seen behind the cannon. The cannon has exhaust fumes coming out in front and the sound it makes is indicated:]
:Cannon: ''Boom''

:[Same setting but the anchor is now under water and the chain has become taut as the ship is dragged forward to the right. Movement lines behind the ship indicated its progress and it is also further into the frame than the previous panel. The movement is caused by pulling the chain back in on the ship. This produces a series of sounds:]
:Dragging chain: ''Click click click''

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Characters with hats]]

3013: Kedging Cannon

2024-11-20T00:32:57Z

172.69.65.224: /* Explanation */

{{comic
| number = 3013
| date = November 18, 2024
| title = Kedging Cannon
| image = kedging_cannon_2x.png
| imagesize = 740x259px
| noexpand = true
| titletext = The real key was inventing the windmill-powered winch.
}}

==Explanation==
{{incomplete|Created by a HEADCANNON. Do NOT delete this tag too soon.}}

Prior to the invention of powered ships, oceangoing vessels moved primarily by means of wind power, which meant that they were restricted by the direction and power of the winds. If a sailing vessel needs travel upwind, they typically make use of a technique called {{w|Tacking_(sailing)|tacking}} (or "tacking against the wind") which involves zigzagging across the wind's direction. This method is significantly slower and more difficult than traveling downwind, but it makes upwind navigation possible.

This comic portrays a fictional scenario where a ship's captain, apparently unfamiliar with tacking, has developed an alternative method based on {{w|kedging}} (also known as warping).

The basics of kedging are not dissimilar to the comic: a boat affixes a rope or chain to an anchor point (such as a literal anchor) and winches itself closer. Traditional kedging involves deploying an anchor from the vessel, either manually or via a smaller boat, and then {{w|winch|winching}} the ship toward the anchor point using ropes or chains. This is a real method, but is clearly very slow and labor intensive. Generally kedging is only effective in shallow waters and employed when tacking is not an option. The captain in this strip appears to be using it for long-distance travel, which would be highly impractical. What's more, he deploys his anchor with a cannon, wasting large amount of gunpowder, all while a confused Cueball looks on wondering why the Captain isn't trying to use tacking instead.

Where the water is too deep for the anchor to reach the bottom, a so-called {{w|sea anchor}} could theoretically be used, but would be even less practical. Kedging with a sea anchor would effectively be a very slow and inefficient version of rowing, which is alternative (albeit labor-intensive) method to travel against the wind.

The title text indicates that the captain's system has evolved to incorporate a windmill mechanism that harnesses wind power to draw in the kedging rope. Windmills are much more intuitive to use for kinetic energy, as the concepts behind the airfoil are very commonly misunderstood as mentioned in a past comic of Randals involving common misbeliefs. The comment brings to mind the comparison of the energy efficiency of a windmill closing a rope vs normal tacking, which different audiences will have different intuitions about, and as such the joke will land differently for different people, but likely this is a ridiculously inefficient rube-goldberg-like solution to wind propulsion, in the context of tacking being discovered, and an ingenious energy saver (if heavy and expensive) in the context of it not. An analysis of the efficiency is below.

{{cot|Speed and economic analysis of dual wind-winched kedging cannons compared to tacking}}
A dual-anchor kedging cannon system for sailing upwind, consisting of:
* Two kedging cannons firing 16 kg anchors
* 6-meter diameter windmill powering winch system
* Dual-winch setup for continuous operation
* Operating in 15 knot headwind conditions

Vessel specifications:
* Length: 30 feet (9.1 meters)
* Displacement: 10,000 lbs (4536 kg)
* Sail area: 600 sq ft (55.7 m²)
* Wetted surface: 40 m²
* Frontal area: 8 m²

;Wind power generation
Available wind power is given by:
''P'' = ½''ρAv''³''η''
where:
* ''ρ'' = 1.225 kg/m³ (air density)
* ''A'' = ''π''(''D''/2)² = 28.3 m² (windmill area)
* ''v'' = 7.72 m/s (wind speed)
* ''η'' = 0.245 (combined efficiency)

This yields 1.95 kW of usable power.

;Drag forces
Total drag combines water and air resistance:
''F''drag = ''F''water + ''F''wind
where:
* ''F''water = ½''ρ''w''C''d''A''w''v''²
* ''F''wind = ½''ρ''a''C''a''A''f''v''²

Using:
* Water density (''ρ''w) = 1025 kg/m³
* Hull drag coefficient (''C''d) = 0.04
* Wetted area (''A''w) = 40 m²
* Air density (''ρ''a) = 1.225 kg/m³
* Air drag coefficient (''C''a) = 0.8
* Frontal area (''A''f) = 8 m²

Total drag force = 1053.4 N

;Anchor ballistics
For 300 m range with 45° launch angle:
* Required velocity = 54.7 m/s
* Launch energy = 23.7 kJ
* Black powder energy per shot = 680.4 kJ
* Launch efficiency = 3.5%

;System performance
* Winch speed = 3.60 knots
* Cycle time = 194.7 seconds
* Effective speed = 3.04 knots
* Compared to tacking speed = 4.95 knots
* Speed ratio (kedging/tacking) = 0.61

;Economic analysis
* Shots needed per nautical mile: 6.1
* Black powder cost per shot: $10 (0.5 lbs @ $20/lb)
* Cost per nautical mile: $60.76
* Powder consumption: 9.2 lbs/hour
* Operating cost: $184.90/hour

Example 100 nmi journey:
* Total powder cost: $6,076.12
* Journey time: 32.9 hours

;Conclusion
The dual-anchor kedging cannon system is both slower and significantly more expensive than traditional tacking:

Speed disadvantage:
* Achieves only 61% of tacking speed
* 100 nmi journey takes 32.9 hours vs 20.2 hours tacking

Economic disadvantage:
* High powder costs ($60.76 per nautical mile)
* Requires significant powder storage (303 lbs for 100 nmi journey)
* Additional wear and tear on mechanical systems

Key limiting factors:
* Limited wind power available (1.95 kW from 6 m windmill)
* High drag forces (1053.4 N total)
* Poor ballistic efficiency (3.5% of powder energy converts to useful launch)
* Long cycle times due to realistic winching speeds

The system could potentially be improved by:
* Larger windmill (though practical size limits on boats)
* More aerodynamic anchor design
* More efficient powder-to-launch energy conversion
* Reduced transfer time between anchors

Therefore, given both the energy constraints and economic factors, traditional tacking remains far more practical for upwind progress. The key insight is that while the kedging cannon seems to "cheat" the wind by going straight upwind, it actually requires converting wind energy to mechanical work less efficiently than a well-designed sail plan, while also consuming expensive gunpowder. The indirect path of tacking makes better use of the available wind force with no consumable costs.
{{cob}}

==Transcript==
:[A two-masted sailing ship with its sails up is floating on a calm sea with tiny waves. Two tiny figures can be seen at the ship's bow. One of them is speaking. In the next panel it becomes clear this is the captain.]
:Captain: I hope someday someone invents a way to sail upwind.
:Captain: Using the kedging cannon just wastes so much gunpowder.

:[Close-up on the deck of the ship, showing two persons behind the taffrail. Cueball is standing behind the ship's captain and talking to him. The captain is wearing a black bicorne navy hat and aiming a cannon containing an anchor forward. Chains are draped from the cannon.]
:Cueball: The '''''what?'''''
:Cueball: Wait, do you not know how to sail upwind? Is that why your ship takes forever to--
:Captain: Stand by...'''''Fire!'''''

:[Distant shot showing the anchor and its chain being launched out in front of the ship, towards the right of the panel. Cueball and the Captain can still be seen behind the cannon. The cannon has exhaust fumes coming out in front and the sound it makes is indicated:]
:Cannon: ''Boom''

:[Same setting but the anchor is now under water and the chain has become taut as the ship is dragged forward to the right. Movement lines behind the ship indicated its progress and it is also further into the frame than the previous panel. The movement is caused by pulling the chain back in on the ship. This produces a series of sounds:]
:Dragging chain: ''Click click click''

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Characters with hats]]

Talk:2736: Only Serifs

2023-02-11T05:42:22Z

172.69.65.224:

first two letters are "A" and "R" I think [[Special:Contributions/172.71.167.10|172.71.167.10]] 04:35, 11 February 2023 (UTC)Bumpf

It's AaBbCcDd. Most likely in Caslon, based on the uppercase A. [[Special:Contributions/172.68.174.149|172.68.174.149]] 04:54, 11 February 2023 (UTC)

So much for a hidden message. [[Special:Contributions/172.68.238.22|172.68.238.22]] 05:05, 11 February 2023 (UTC)

If we've come to this page for an explanation, we probably don't know what a "solum-serif font" is. update the transcript with something more widely known? [[Special:Contributions/172.69.65.224|172.69.65.224]] 05:42, 11 February 2023 (UTC)