Difference between revisions of "3013: Kedging Cannon"

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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, which makes the solution even less efficient, given that wind could be used for tacking.
 
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, which makes the solution even less efficient, given that wind could be used for tacking.
 +
 +
{{cot|Speed and economic analysis of kedging cannons compared to tacking}}
 +
;System Overview
 +
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
 +
 +
;Physics Analysis
 +
 +
;Wind Power Generation
 +
Available wind power is given by:
 +
P = ½ρAv³η
 +
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 = ½ρ_w C_d A_w v²
 +
* F_wind = ½ρ_a C_a A_f v²
 +
 +
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 300m 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 100nm 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:
 +
 +
1. Speed disadvantage:
 +
* Achieves only 61% of tacking speed
 +
* 100nm journey takes 32.9 hours vs 20.2 hours tacking
 +
 +
2. Economic disadvantage:
 +
* High powder costs ($60.76 per nautical mile)
 +
* Requires significant powder storage (303 lbs for 100nm journey)
 +
* Additional wear and tear on mechanical systems
 +
 +
3. Key limiting factors:
 +
* Limited wind power available (1.95 kW from 6m 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.
 +
{{cab}}
  
 
==Transcript==
 
==Transcript==

Revision as of 04:11, 19 November 2024

Kedging Cannon
The real key was inventing the windmill-powered winch.
Title text: The real key was inventing the windmill-powered winch.

    Explanation

    Ambox warning blue construction.svg This is one of 57 incomplete explanations:
    Created by a HEADCANNON. Do NOT delete this tag too soon. If you can fix this issue, edit the page!

    Sailing vessels can navigate upwind through a technique called tacking (or "tacking against the wind") which involves zigzagging across the wind's direction. However, this comic describes a fictional scenario where a ship's captain, unfamiliar with tacking, has developed an alternative method based on kedging.

    Kedging is a historical maritime technique typically reserved for specific situations where conventional sailing methods are impractical, such as in calm waters, during precise maneuvering, or against strong opposing winds or currents. Traditional kedging involves deploying an anchor from the vessel, either manually or via a smaller boat, and then winching the ship toward the anchor point using ropes or chains. The anchor points often utilize natural features such as trees or reefs. In this comic, the captain has modified this technique by inventing a specialized "kedging cannon" to project the anchor greater distances.

    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, which makes the solution even less efficient, given that wind could be used for tacking.

    Speed and economic analysis of kedging cannons compared to tacking
    System Overview

    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
    Physics Analysis
    Wind Power Generation

    Available wind power is given by: P = ½ρAv³η 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 = ½ρ_w C_d A_w v²
    • F_wind = ½ρ_a C_a A_f v²

    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 300m 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 100nm 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:

    1. Speed disadvantage:

    • Achieves only 61% of tacking speed
    • 100nm journey takes 32.9 hours vs 20.2 hours tacking

    2. Economic disadvantage:

    • High powder costs ($60.76 per nautical mile)
    • Requires significant powder storage (303 lbs for 100nm journey)
    • Additional wear and tear on mechanical systems

    3. Key limiting factors:

    • Limited wind power available (1.95 kW from 6m 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. Template:cab

    Transcript

    Ambox warning green construction.svg This is one of 30 incomplete transcripts:
    Do NOT delete this tag too soon. If you can fix this issue, edit the page!
    [A two-masted sailing ship is floating on the sea. Two tiny figures can be seen at the ship's bow.]
    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. Cueball is talking to the ship's captain, who is aiming a cannon containing an anchor. 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.]
    SFX: BOOM
    [The line becomes taut and the ship is dragged forwards, towards the right of the panel.]
    SFX: Click click click

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    Discussion

    First? PRR (talk) 02:05, 19 November 2024 (UTC)

    Good essay on real-life (or this-world) kedging-- http://www.sailmagazine.com/cruising/cruising-tips/the-lost-art-of-kedging-how-to-set-a-kedge-anchor/ PRR (talk) 02:07, 19 November 2024 (UTC)

    Nice. I think I managed to somehow get in first (before I logged in); first time I've done so, so apologies for not knowing all the conventions. I think the title text is the main non-obvious thing, since the simile between a windmill's mechanical function and that of tacking seems clearly intentional,but I'm sure that could be edited to be clearer than my hasty writup. Mneme (talk) 02:10, 19 November 2024 (UTC)

    For a brief, brief, moment, my brain failed to swap in and dredge up the memory of what kedging was, and I wondered if they were trying to use the aft cannon as a weak propulsion mechanism (hey, if it was a spacecraft…). And then I remembered what kedging was and—DUH! JohnHawkinson (talk) 02:29, 19 November 2024 (UTC)

    If it wasn't for kedging, I probably wouldn't be able to make it all the way through November. 108.162.245.133 04:25, 19 November 2024 (UTC)

    Ha ha now exactly what you mean. The three longest month of the year are November November November... :-) --Kynde (talk) 10:05, 19 November 2024 (UTC)
    Having a certain number of winches helps. 172.68.23.92 10:44, 19 November 2024 (UTC)
    My birthday is in November, helps a lot. 172.71.150.108 00:10, 20 November 2024 (UTC)

    Wow, whoever wrote the Speed and Economic Analysis section, you are amazing! 172.71.98.135 05:13, 19 November 2024 (UTC)

    Sadly is was done by an anonymous IP address... But cool analysis. Have no idea what he actually calculates or if it is correct though ;-) --Kynde (talk) 10:05, 19 November 2024 (UTC)
    The system described doesn't need two cannons, just two anchors and winches for continuous operation. As something of an anonymous IP address editor myself, I am checking the math and intend to parameterize the assumptions for different size boats, different headwinds, and other different parameters. If I am successful, I will log in to upload a graph showing when cannon kedging is superior (if it ever is....) 172.68.23.92 10:44, 19 November 2024 (UTC)
    I don't see depth of the water in the calculation. In the limit, if the anchor is snagging something at the surface of the water, the ship moves forward 300 m per shot. If the anchor is snagging something very very deep, the ship moves forward 0 m per shot. I kinda suspect that there's some assumption built in, and that's what's showing up as the effective speed, but not sure. 162.158.154.6 21:47, 19 November 2024 (UTC)
    If you're adding to the calculations ... I also don't see a bottom line calculation for the tacking speed, unless I'm just missing it? There's a statement that kedging is 61% of that speed, but I can't see where/how the tacking speed was calculated. My intuition is screaming that over half the speed of tacking against the wind has got to be a mistake of some kind, but my intuition has certainly betrayed me before. The idea that maybe you can anchor to the surface of the water does seem like a good place to look for a hidden assumption!172.69.130.116 12:18, 20 November 2024 (UTC)

    I've got a strong hunch that this comic is about a captain who fails to take into account recoil / conservation of momentum, which is a frequent mistake. The cannon propels the anchor with great force, but, as it is connected to the ship, the ship is pushed back with the same force (minus some heat losses) before the anchor can settle. Therefore, in this setup the ship will only move forward at all if the anchor ends up at a greater horizontal distance from the ship's original position than the distance between the ship's original and post-cannonshot positions. The third panel, where the ship is drawn further to the left, indicates that the setback is significant and the ship only moves back and forth in the same place. Like, it literally takes forever. The title text is a hint: Only if the captain manages to harness a source of power that is independent from the vessel's movement (for example: wind from the wrong direction) this cannon will have any propagating effect - using this power for the winch, however, is just as futile as the kedging cannon itself. For manual kedging, people heave the anchor to a boat and row out to a drop site, so it's not an issue. Or am I missing something? Transgalactic (talk) 11:07, 19 November 2024 (UTC)

    No, this is incorrect; the center of mass of a kedging ship + anchor does not stay in the same place - the anchor has caught on some feature of the seabed so the CoM can move towards the anchor as it is winched in. Even a sea anchor would work so long as the drag in water is sufficiently greater than the drag in air, but at that point you're evolving towards re-inventing the oar.
    As the ship is much heavier than the anchor and it additionally experiences resistance from the water, the amount the ship moves back is much less than the amount the anchor moves forward. I don't know if the ship being drawn further to the left is supposed to indicate that it moved backwards, but even if you assume that the frames are supposed to represent the same area of the ocean (which would imply the ship has moved backwards) you can see that the anchor has landed to the right of the frame, so the ship will have moved forward at the end of the manoeuvre. 172.68.205.92 12:03, 19 November 2024 (UTC)
    I think the objection is based upon the "on a frictionless surface in a vacuum" thought experiment whereby you try to make progress from continually throwing a tethered object (with insufficient reach to get to the edge of said frictionless surface) then drawing it back in again. With absolutely nothing to assymeyrically provide grip, even throwing it out fast then drawing it back slowly won't get you either towards or away from the direction of throw after each complete cycle. (Whereas if you untethered it, or let the tether snap, you would at least get some residual frictionless+resistanceless Newtonian movement out of it and could coast back against the thrown direction until you sufficiently escaped the frictionless area.)
    Of course, in the sea-going example there's various resisting effects that you can use to your advantage (assuming there aren't active wind/water effects sufficient to overcome your desired vector of gains). Either differential between air and water (sea-anchor flies out with less resistance than it encounters when you drag it back in, or just set up something to row/paddle-wheel the same sort of effect of uneven push/pull reciprocation), an assymetrically varying object of resistence (opening/closing umbrella, parachute envelope or, potentially again, sea-anchor equivalent), an off-direction effect that creates a perpendicular force you require "waggly-tail" oaring, or how a boat stays upright so that a relatively turning screw creates propulsive thrust) or even use time-/force-dependent viscosity (shoving hard in one direction creates a different total resistance from pulling the exact same (directionally agnostic) mass softly back again in the opposite direction; rinse and repeat to accumulate whatever differential effect that you generate). Several other options suggest themselves, with fully closed-cycle reciprocations.
    Though what we have here is a partial 'open-cycle' system. The expelled 'exhaust' of the fired cannon actually acting against the throw-and-drag process, but probably only marginally, and could be factored in as a beneficial force either by using sufficient waste-gas "blow back" diverters to extract cannon-direction momentum (not just recoilless, but 'anti-directional recoil', like jet engine reverse-thrust 'scoops' do to aid deceleration once safely touched down upon landing) in just the right way or where the "firing is through a hard medium, but the pull-back is through an easy one" (e.g. direct your projectile directly out-but-down into the water, but have it buoyant enough to breach the surface (or even rise, Zeppelin-like, completely out into the air!) so you can retrieve it with far less dragging effort - then you're travelling in the opposite direction from what you're firing, adding 'redeployable thrust' to the expended 'rocket reaction thrust').
    Anyway, all that aside, I think that's where Transgalactic was headed (their original "am I missing something?" bit, before all my "no, except..." caveats as to various possible missing bits). Hopefully helps a bit. Even if none of it technically helps in a totally reactionless (non-depleting) space-thrusting scenario, which of course would be a useful thing to have. (We probably need a way to decouple gravitational mass from inertial mass, and selectively so, to do that!) 172.70.46.222 13:43, 19 November 2024 (UTC)

    Maybe instead of using a cannon, we could use a ballista? Saves gunpowder, but requires human labor. I think that would still be more efficient. --Coconut Galaxy (talk) 11:44, 19 November 2024 (UTC)

    It would be more efficient to have the sails furled. Every time the anchor is lifted the wind will push the boat back again. 172.69.214.135 (talk) 12:27, 19 November 2024 (please sign your comments with ~~~~)

    It is definately not visible, but I'm pretty sure there is a beret hiding under that hat. 162.158.10.188 18:58, 19 November 2024 (UTC)

    That was my first thought. 172.71.150.108 00:10, 20 November 2024 (UTC)

    The sailing rig drawn is approximately a "2 masted schooner". There were MANY variations and add-ons in schooners, few this simple, but Munroe is making funnies not a treatise on sailing ships.

    Schooners generally are better for 'tacking upwind' than square-rig, while potentially limiting the amount of manpower needed and spar-weight up high.

    Yes, kedging will work in any wind or no wind, so this is a superior solution, until the powder runs out. PRR (talk) 22:44, 19 November 2024 (UTC)

    My thought at the line `Is that why your ship takes forever to--' was that the ship was the `Flying Dutchman' taking forever to round the cape. Lordpishky (talk) 01:25, 20 November 2024 (UTC)

    Cable ferries are not just for crossing rivers - they can also be used in the sea, such as the Baynes Sound Connector 172.68.22.83

    Fun fact kedging is obscure enough that searching just the word kedging returns this page as a result172.70.211.99 18:53, 28 November 2024 (UTC)
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