Factors affecting Cannonball Range

[Poyraz]

As far as I experienced, right now we have a major effect of heeling on cannonrange. Example is if you are upwind of your opponent, when shooting, your ship heels towards your target which reduces the angle of your cannons, thus the effective cannon range. Everything is fine until here.

 

My concern is though, the kinematic of cannonballs after they got fired. And the leading role here is the air resistance. Before going further, here is a good read if you are not familiar with the physics.

 

Lets say the cannonball has an average speed of 115m/s.

 

Now the downwind ship has the advantage of heeling, whereas it also has the disadvantage of firing cannons against the wind. Lets assume wind speed is 10 knots which is approximately 5m/s. The relative wind, which affects the cannonball speed exponentialy, is now 115 + 5 = 120m/s. This adds an extra 5m/s air resistance component to the cannonball.

 

On the other hand, the ship firing from upwind to a downwind target with the wind will have 5m/s less air resistance when shooting a cannonball. This results in, the relative wind to this cannonball being 115 - 5 = 110m/s. To visualise the affect of air resistance you can use this simulation.

 

Red without, Blue with air resistance

 

In this example, the difference of the air drag's of those two different cannonballs is around 29%. In other words, there is an 29% extra force, trying to stop the cannonball and reducing its range.

 

Now, if we come back to the game mechanics, I think the air resistance (drag) effect should compansate the range increase due to heeling angle, thus making both ships having same range no matter downwind or upwind.

 

 

 

 

 

 

 

[Clinch]

I was just thinking about this yesterday. In the current build, the ship that is downwind has an advatage in range while the captain holding the weather gage is at a disadvantage. Good post Poyraz.

[maturin]

I have a hard time believing that 10 kts of wind is going to balance out 10 or more degrees of barrel elevation. You should do the math and then suggest this.

[Poyraz]

I have a hard time believing that 10 kts of wind is going to balance out 10 or more degrees of barrel elevation. You should do the math and then suggest this.

 

Well, that is aerodynamics and is exactly why a Boeing 777 with its 351.000kg mass can fly in the skies. Air under high speed acts like a more dense fluid e.g. water.

 

If you would read the reference I have given in the original post, you would see the formulas and calculations, but here they are again:

 

It looks like the starting speed is between 100 m/s and 200 m/s (if I ignore air resistance). And that is the question: Can I ignore air resistance? To do this, I first need to make some assumptions about the ball. Here are my guesses.

• Let me use a ball diameter of about 11 cm. I get this by looking at the barrel size in the photo with Tory Belleci above.
• The ball is made of iron with a density of 7,860 kg/m³. This would make the mass of the cannon ball 5.5 kg.
• The ball is a smooth sphere with a drag coefficient of 0.47.
• One last assumption. Let me assume that the cannon ball was moving slow enough that the typical model for air resistance works.

One simple way to see if you need to include air resistance is to calculate the magnitude of the air resistance force for the speeds the ball will be moving. If the air resistance is small compared to the gravitational force, it might be ok to ignore it. Here is the usual model for the magnitude of the air resistance force.

The key thing here is the v² term. If I use 200 m/s and the data above, I get an air resistance force of 107 N. The weight of the 5.5 kg ball would be just 53 Newtons. This means I cannot ignore air resistance. Bummer.

 

 

I will try to elaborate the example in OP deeper here, to make it more clear.

 

1. The effect of 10 knots wind will be doubled first, because it,

• increases the relative wind of the cannonball from the ship in downwind firing to upwind in 5m/s  ==> V1_relative = 120m/s
• decreases the relative wind of the cannonball from the ship in upwind firing to downwind in 5m/s ==> V2_relative = 110m/s

2. The effect of the those winds will than exponentialy increase the air resistance due to the factor V². If you place the parameters in the equation below:

 

 

As a result, we will have the air resistance for those firing ships as, F_{air, V1}= 40N and F_{air, V2}= 33N.

 

I agree with you on one point though, because there was a typo in the original post. The ratio difference (F_{air, V1} / F_{air, V2}) of the air drag's of those two different cannonballs is around 19%, not 29%, which will than linearly affect the range.

 

In conclusion, if the fact, that a 5,5kg cannonball would hit the land after being fired from a cannon with the gravity effect of 53N is believable, then the fact, that the air resistance of 40N trying to stop it, reduces its range more than a 33N air drag, should also be believable.

 

Comparison of Air Drag with Heeling Angle:

 

Now, some data on the firing angle which is increased due to the heeling of the ship:

 

Fire Angle      Range[m]      Effect on Range of every 10° Elevation

     10° ------------- 325

     20° ------------- 427 --------------------------- 31%

     30° ------------- 476 --------------------------- 11%

     40° ------------- 484 ---------------------------   1%

     50° ------------- 453 ---------------------------  -7%

 

 

As seen in the table as well as in the picture, the heeling angle has a progressively decreasing effect. I think trying to model the heeling effect is a good approach for realism. But as it is implemented like right now, it creates unrealistic behaviour on the contrary, without considering and modeling the air drag.

[maturin]

So 10 kts of wind causes 19% disparity and 10 degrees of heel can cause over 30% disparity. Elevation wins out, and the leeward vessel would outrange its opponent in this case.

If the windward vessel could only elevate its guns to 0 degrees, the difference would be enormous.

[Poyraz]

So 10 kts of wind causes 19% disparity and 10 degrees of heel can cause over 30% disparity. Elevation wins out, and the leeward vessel would outrange its opponent in this case.

If the windward vessel could only elevate its guns to 0 degrees, the difference would be enormous.

 

Not exactly.

First thing first, there is a mathematical correlation between the wind speed and heel angle. The more wind, the more heeling or vice versa, more heeling means stronger wind. So, you just can't compare high heeling anlges with slow wind speeds.

Now if we talk about HMS Victory, a 10° of heel angle for Victory is at the limits, because at this angle Victory begins to take water from the lowest gunports. (Source)

And the heeling (rolling) of the ship depends on:

• Wind speed
• Projection area of the ship (Mostly sails),
• Wave action,
• Any centrifugal force developed in turning,
• Uneven mass distribution in the ship.

To heel HMS Victory 10 degrees, lets say 20 knots of wind is necessary. This is the double of the wind example in the OP. And due to the facto V², it will affect the air drag exponentialy. As a result with the same formulas above, we would find downwind ship having 42% more air drag against his cannonballs.

 

About the projection area of the ship, we can say if the ship upwind go battle sails or lower all sails reducing the most of the heel caused by wind, right at this point, it could have even more range than the downwind ship with the effect of less heeling combined with relative less air drag.

 

Wave action would be similar for each ship. I am not sure the effect of wave rolling is implemented though.

 

Both ship can also induce more heel angle due to centrifugal force developed in turning, if they turn in direction of each other.

 

As uneven mass distribution, the example of captain stacking the provisions or ammunitions in the not firing opposite broadside can be given.

 

In conclusion, I still think the cannon range of the ships should stay ineffected and same for more realistic and fun gameplay.

 

Another site note: Those firing angles and air drag have another effect which is the trajectory curves of the cannonballs. With the effect of high heel angles and relative higher air drag, the cannonballs from downwind ship will have less velocity and more angle at the point of impact.(Howitzer in the picture) On the otherhand, the cannonballs from upwind ship would follow a curve like the cannon/gun in the picture having less angle and more velocity on the point of impact. This effect could be considered in the damage model.

 

[PIerrick de Badas]

I don t Know if someone hère has évier play airsoft. Thérèse is a systèm called hop up that make turn the ball and it s cage the distance that is almost dubble althought it décreuse the speed of the ball.

You CAN t compare à round shot and à Boeing be cause the ball is round and don t get the same aerodynamism as à plane. It s something spécificité and if info the gun something make the roundshoot turn, it s also going to change the range.

Another solution is to adapt worms artillery with bazooka in na

[Poyraz]

Those differences are considered with the air coefficient "C" and the area "A".

 

The air drag parameter is a complex one though, and were measured in wind tunnels for any given geometry like sphere.

[Privateer]

Poyraz raises an excellent point, and I commend the citations.  The weather gage is a key advantage in fair weather, but under extreme conditions can be to one's own detriment.  Apart from reduced firing elevation, lower gunports can become awash.  This reduces the number of effective guns that can be brought to bear while underway. 

 

If I recall, the ship's moment of force depends primarily on the distribution of sail area.  At full canvas the ship experiences the greatest amount of heel not only because of an increase in overall force, but as a compounding effect of an increase in the moment of force.  Consider a mast with only its course set, all others furled.  The moment of force will be low on the mast, close to the hull (and, thus, the center of mass).  Conversely, a mast with only its topsails set will experience a higher moment of force, well above the center of mass, and higher still for gallants and royals, etc. 

 

It stands to reason that, for an equivalent amount of sail area, the course will impart less heel than gallants or royals in arbitrary conditions, meaning that a leeward opponent would (in theory) favour the use of upper sails with the inverse true for the opponent to windward.  In practise this may not be the case, as the reliability of rigging is roughly inversely proportional to its distance from the hull.

 

Am I correct in assumption?

[maturin]

Sailing under courses alone was unheard of after the first few decades of the 18th century. Both fleets would always have their topsails set, and the leeward fleet would not be particularly interested in heeling, as it just makes things difficult. If you are availing yourself of the leeward range advantage, you are probably too far away to hit much of anything anyhow.

 

If you want to reduce heel, you can simply shiver the topsails by rotating the yards. This will cause you to decelerate after a moment, but the effect on heeling will be instant. (In the game, heel is still incorrectly tied to speed, which handicaps players.)

[Privateer]

That makes sense.  I wasn't certain as to how NA was handling heel.  The topsails are less likely to take hits and are comparatively easier to trim (ideal when able crew is in short supply), and with further reading I gather that staysails were more reliable in heavy weather, as their use was more conducive to precision heading when the squares became quite cumbersome.  You could aways time your shots with the roll of the waves, failing all else.

[Barberouge]

So the lee side has advantages at distance, be it due to longer range, too tight shot spread, low wind effect or no requirement to decrease speed. Since the weather side sometimes can't use lower gun ports but keeps the initiative, I think it would be fair to remove the lee range advantage. Then it should be tested in mass battles.

[Edward Vernon]

I think you are all being a bit too simplistic here. In reality it would be a combination of all those things, some more or less than others. For example the differential in size and weight of shot and powder load is ignored. Heel angle is not constant and a clever captain will negate that by careful manouevring of his ship to take off negative heel angle and maybe even add positive at the moment of firing, if that is to his overall tactical advantage. One way of doing this would be to let fly the sheets at the moment critique, at the cost of loss of speed. Now accepting that all of these variables would be very difficult to model realistically, the actual ballistics model will be an approximation I would expect along with the chance variables (RNG) for things such as the variable roundness of shot and the rough or smoothness of the finish on the shot. Remember that it was not uncommon for sailors before a battle to be set to chipping rust off round shot to make them less subject to variances but this very act would also marginally and randomly reduce the weight of shot.

 

Privateer writes... about the moment of force being primarily dependent on the distribution of sail area.....but that is only half. It also depends on the position of the C of G (Centre of Gravity) about which the moment operates, this will alter according to any number of factors, so again a simplistic model will, I expect be used.

 

In sum, I would suggest that we let the devs do their thing and then once we have sampled what they produce then suggest improvements, and whilst, detail, knowledge and mathematics are all wonderful things along with the passion you all obviously have for this game I think you may just be going TOO far down this particular rabbit hole.

[Barberouge]

Heel angle is a factor in game already. Letting the sheets fly isn't possible, but rotating the yards is. Thus what you describe (sacrifice some speed to get appropriate range) is a viable tactic. About balistics, you can check this topic: Naval Action - Cannons.

 

Then about windward/lee range, it's also about gameplay (not only mathematics).

[Edward Vernon]

Thanks Barberouge. The topic you linked pretty much confirms what I said. Also I could not agree more that at the end of the day it is about gameplay not just mathematics and by the look and sound of it you should be there with your current solution.

[admin]

If you want to reduce heel, you can simply shiver the topsails by rotating the yards. This will cause you to decelerate after a moment, but the effect on heeling will be instant. (In the game, heel is still incorrectly tied to speed, which handicaps players.)

 

Heel is tied to wind angle not speed, it probably feels this way because when you lower sails you reduce wind pressure - thus lowering heel.

 

If there are examples of wrong heel please post screens here. will review as it is definitely a bug then.

[maturin]

Heel is tied to wind angle not speed, it probably feels this way because when you lower sails you reduce wind pressure - thus lowering heel.

If there are examples of wrong heel please post screens here. will review as it is definitely a bug then.

Whatever heel is tied to, the problem is this:

If I turn my yards parallel to the wind, heel reduces only slowly. I have to lose 3-4 knots before I see a serious difference. But the change should start instantly, because gravity tries to keep the ship upright. If the wind force decreases, the ship will almost instantly start to straighten up.

As for heel and wind angle, I have already posted a detailed diagram somewhere.

But the short version is this:

The game should swap the current closehauled and beam reach heel angles. If the ships were to heel on a beam reach the same way they do when closehauled (and vice versa), that would be a big improvement.

It's hard to explain. Is that clear?

[admin]

As for heel and wind angle, I have already posted a detailed diagram somewhere.

 

 

on the switch of heel. a picture would be very helpful. 

[Barberouge]

In this link, you can check the 2nd diagram of page 23 to see the heel force curve. The page 24 gives rig variations. And the diagram of page 27 shows the effect of changing the yard angle.

[maturin]

on the switch of heel. a picture would be very helpful.

http://m.imgur.com/fw72TGV,mJK1VSd

^

Combined explanation of heel/roll.

[admin]

http://m.imgur.com/fw72TGV,mJK1VSd

^

Combined explanation of heel/roll.

thanks man

[Poyraz]

Heel is tied to wind angle not speed, it probably feels this way because when you lower sails you reduce wind pressure - thus lowering heel.

 

If there are examples of wrong heel please post screens here. will review as it is definitely a bug then.

 

I agree that heel is a function of wind angle.

 

However, as you said, it also indirectly related to the speed. Because the keel effect of underwater hull decreases with lower speeds and increases with higher speed values. So, less speed means less force for balancing the heel effect, which means more heeling.

 

Considering the same wind angle, to decrease speed the sails should be lowered or rotated. This also reduces the heel force, which reduces the heel moment and heeling itself.

Active stabilizers are most effective at maximum vessel speed, less so at lesser speeds, minimally effective with no forward speed.

The same goes for rudder. High speeds mean more turning, less speeds mean slow turning and rudder has no effect at all while standing still.