# Rudder force

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After 10 months of developing something else i finally have some time to write my game. i have two questions

first main question:

based on picture below which arrow defines proper force acting on ships rudder?

green or red?

cause when i use green i cant make it turn maybe i have too small rudder area (thats the second question: whats the size of a rudder lets say for a frigate)

as far as i remember green one was supposed to be correct one (drag acts always in opposite of velocity)  but what do i know after 10 months of nothing. ;x

Edited by WiredCat

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It's not the green arrow. That's like putting a ball on a slope and saying "it won't gain any X velocity because gravity is only acting in the Y direction." Edited by Nypyren

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as the ship moves forward, the rudder diverts the flow to the left, so the water "pushes" the rudder in the direction of the red arrow., thus pushing the rear of the ship to the right, causing the ship to turn left.

F_on rudder = f(V, rudder_angle)

turn rate = f(F_on_rudder, ship_rotational_inertia)

V is the velocity of he ship thru the water.

the force on the rudder is a function of V and the rudder angle (more angle = more force).   might try 1/10th V * cos (rudder_angle) to start.  or do the physics,   but particle flow simulation is complex!

the turn rate is a function of the force on the rudder, and the rotational inertia of the ship (IE how heavy it is) . (maybe try 1/10th  F_on_rudder, but that may be too low. and bigger ships turn slower at a given speed and rudder angle).

rapid prototyping is called for to determine the correct values empirically.  but you can also look up the physics behind it all, but fluid mechanics can be complex.

Edited by Norman Barrows

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still im not convinced that red arrow is correct, on all books i read about making flightsim i saw that drag (even one from that rudder) should act in velocity opposite direction.  :unsure:  :wacko:  :blink:

Edited by WiredCat

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Drag acts in the direction of the green arrow but drag isnt what makes the ship turn. The red arrow decompose into a drag force (green arrow) and a steering force (not in the picture, but should point to the right)

The rudder works like a wing, I guess you could call the red arrow the "lift" of the rudder

Edited by Olof Hedman

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The rudder will work like a wing - which means:

1. Sometimes there will be laminar flow over it, and sometimes it will be stalled.

2. The forces on the rudder can be calculated as the sum of the lift force (which always acts in a direction perpendicular to the fluid flow relative to the rudder - so it's not the red arrow, but will act directly to the right in your diagram, given the blue arrow is pointing "up"), and the drag force (which always acts in a direction opposite to the fluid flow). These forces will be proportional to the square of the (local) fluid speed, the rudder area, and the coefficients of lift and drag.

You need to remember that you need to calculate the local fluid flow velocity at the rudder. When the boat is turning, this will not just be -v.

You can actually estimate these coefficient of lift (CL) and drag (CD) values pretty accurately - but you might need to do so over the whole 360 degrees - i.e. you need to know CL and CD  as a function of angle of attack. I'd expect them to look rather similar to curves in air - so if you have something that looks like this it should work OK: http://www.aerospaceweb.org/question/airfoils/q0150b.shtml

Alternatively, if your boat has got a keel, when the fluid flow is significantly from the side, the effect of the rudder is probably minimal - in which case you only need to calculate the rudder force when the flow is laminar. For this CL is going to be directly proportional to alpha (the angle of attack) up to around +/- 15 degrees or so - then the rudder will stall and you can set it to zero. CD will be something like constant + alpha^2 up to the same angle (and beyond that you could clamp it).

This might all be overkill if you're not trying to do anything like a proper boat simulation :) If you want something simpler, just making the torque proportional to the rudder deflection and forward speed will probably work (assuming you have another rotational damping term that represents the reluctance of the boat (due to the keel) to turn when moving fwd/back).

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The rudder will work like a wing - which means:

1. Sometimes there will be laminar flow over it, and sometimes it will be stalled.

2. The forces on the rudder can be calculated as the sum of the lift force (which always acts in a direction perpendicular to the fluid flow relative to the rudder - so it's not the red arrow, but will act directly to the right in your diagram, given the blue arrow is pointing "up"), and the drag force (which always acts in a direction opposite to the fluid flow). These forces will be proportional to the square of the (local) fluid speed, the rudder area, and the coefficients of lift and drag.

You need to remember that you need to calculate the local fluid flow velocity at the rudder. When the boat is turning, this will not just be -v.

You can actually estimate these coefficient of lift (CL) and drag (CD) values pretty accurately - but you might need to do so over the whole 360 degrees - i.e. you need to know CL and CD  as a function of angle of attack. I'd expect them to look rather similar to curves in air - so if you have something that looks like this it should work OK: http://www.aerospaceweb.org/question/airfoils/q0150b.shtml

Alternatively, if your boat has got a keel, when the fluid flow is significantly from the side, the effect of the rudder is probably minimal - in which case you only need to calculate the rudder force when the flow is laminar. For this CL is going to be directly proportional to alpha (the angle of attack) up to around +/- 15 degrees or so - then the rudder will stall and you can set it to zero. CD will be something like constant + alpha^2 up to the same angle (and beyond that you could clamp it).

This might all be overkill if you're not trying to do anything like a proper boat simulation :) If you want something simpler, just making the torque proportional to the rudder deflection and forward speed will probably work (assuming you have another rotational damping term that represents the reluctance of the boat (due to the keel) to turn when moving fwd/back).

^this. you are correct in understanding the drag opposite velocity, but you need to account for the effect that force has on the rudder. the rudder directs the flow to the left, which creates an opposite force on the rudder, pushing the rear of the boat to the right. There is a ton of good info on the web about this stuff. I know that "https://www.amazon.com/Physics-Game-Developers-David-Bourg/dp/0596000065" does a decent job of describing the background math behind this problem, check your local library

Edited by Burnt_Fyr

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