Quantifying the difference of drag between a 15.5mm and 19mm mast, here is how I did it, please let me know if you think the calculation is incorrect!

The drag of the whole setup is D = V^2 * S * Cd. Assuming we just swap masts with similar profiles, there is no change in lift, and we have the same speed V and coefficient of drag Cd, so the difference is the change of surface area, seen from the front of the foil.

Taking a photo from the front of the foil and measuring surfaces in cm^2 with sketchandcalc website (Takuma kujira 1210, aluminum mast 75, 178 tail), I get :
Half mast : 35 (5 if almost all out, to 60 if almost fully immersed)
Front wing : 144
Fuse and tail : 26
Total : 205 cm^2

If 15.5mm thickness gives 35 cm^2, 19mm gives 43 cm^2 (cross-multiplication). The total surface would then be 213 cm^2, meaning a 3.9% drag increase (0.6% if almost all out, to 6.1% if almost fully immersed).

What if the front wing gets smaller? With the 980, same process I get 4.1% drag increase (0.6% if almost all out, to 6.4% if almost fully immersed).

I hope the calculation is correct, and I hope it helps other people out there to have a proper framework on drag difference between 16 and 19mm masts!

Playing around with foil sim www.grc.nasa.gov/www/k-12/airplane/foil3.html

you can set it up as water and make the span/chord/thickness match different wings. I set up a wing, then dial low speed(10kts), then dial the angle to produce a lift equivalent to my weight. Note the drag, then do the same at a higher speed. (25kts)

Setting it up as a mast (no angle, ignore lift) you can see how thicness to chord impacts drag at different speed.

Thickness doesn't make a big difference at low speeds but makes a significant difference at high speed. Again, this isn't a perfect model but its fun.

Drag coefficients can use different area definitions. For example for a blunt body such as a car you might specify the drag coefficient in terms of projected frontal area.

for wing profiles, drag coefficients are typically based on the surface area of the wing, not the projected frontal area, as this way, the area term used is the same as the area used to calculate lift or induced drag.

see en.wikipedia.org/wiki/Drag_coefficient for confirmation of this:

'The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere wikimedia.org/api/rest_v1/media/math/render/svg/33f7b7f93f93e7ba7bebb97efbe88e181ce332e4 (note this is not the surface area = wikimedia.org/api/rest_v1/media/math/render/svg/b81fcce302776a01dc66fc186a1ce0a616b4d772).

For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed."

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TooMuchEpoxy said..
Playing around with foil sim www.grc.nasa.gov/www/k-12/airplane/foil3.html

you can set it up as water and make the span/chord/thickness match different wings. I set up a wing, then dial low speed(10kts), then dial the angle to produce a lift equivalent to my weight. Note the drag, then do the same at a higher speed. (25kts)

Setting it up as a mast (no angle, ignore lift) you can see how thicness to chord impacts drag at different speed.

Thickness doesn't make a big difference at low speeds but makes a significant difference at high speed. Again, this isn't a perfect model but its fun.

Thank you for the idea! I set the parameters as follows :
- Front wing ~Game changer 1260 : Thick/Chord ratio 2.5%, Chord 0.5ft, Span 2.7ft, AR 5.4, 2cm thick
- Stab : Thick/Chord ratio 2.5%, Chord 0.2ft, Span 1.1ft, AR 5.5, 2 degres of angle
- Mast 16mm : Thick/Chord ratio 13.3%, Chord 0.4ft, Span 1.3ft (~half mast). CDrag 0.024 at 10kts.
- Mast 19mm : Thick/Chord ratio 15.8%, Chord 0.4ft, Span 1.3ft (~half mast). CDrag 0.029 at 10kts.

It gives a 5 to 8% difference of drag in the 7-25kts range of speed, I think most action proning happens around 10-15kts. Let me know what you think, also if the current parameters I use are valid(?). Current drag results below :

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Pacey said..
Drag coefficients can use different area definitions. For example for a blunt body such as a car you might specify the drag coefficient in terms of projected frontal area.

for wing profiles, drag coefficients are typically based on the surface area of the wing, not the projected frontal area, as this way, the area term used is the same as the area used to calculate lift or induced drag.

see en.wikipedia.org/wiki/Drag_coefficient for confirmation of this:

'The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere wikimedia.org/api/rest_v1/media/math/render/svg/33f7b7f93f93e7ba7bebb97efbe88e181ce332e4 (note this is not the surface area = wikimedia.org/api/rest_v1/media/math/render/svg/b81fcce302776a01dc66fc186a1ce0a616b4d772).

For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed."

The calculation would be more accurate with a dedicated drag coefficient for each mast instead of assuming they have the same. The nasa foil sim allows to get the drag coefficient of the masts (0.024 and 0.029 at 10kts), but not the whole setup. In the equation D = V^2 * S * Cd, Cd is for the whole foil. Not sure how the coefficients of the front wing, stab and mast combine to get Cd ?

Select to expand quote

foilstate said..

Pacey said..
Drag coefficients can use different area definitions. For example for a blunt body such as a car you might specify the drag coefficient in terms of projected frontal area.

for wing profiles, drag coefficients are typically based on the surface area of the wing, not the projected frontal area, as this way, the area term used is the same as the area used to calculate lift or induced drag.

see en.wikipedia.org/wiki/Drag_coefficient for confirmation of this:

'The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere wikimedia.org/api/rest_v1/media/math/render/svg/33f7b7f93f93e7ba7bebb97efbe88e181ce332e4 (note this is not the surface area = wikimedia.org/api/rest_v1/media/math/render/svg/b81fcce302776a01dc66fc186a1ce0a616b4d772).

For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed."

The calculation would be more accurate with a dedicated drag coefficient for each mast instead of assuming they have the same. The nasa foil sim allows to get the drag coefficient of the masts (0.024 and 0.029 at 10kts), but not the whole setup. In the equation D = V^2 * S * Cd, Cd is for the whole foil. Not sure how the coefficients of the front wing, stab and mast combine to get Cd ?

The front wing coeficient would be all over thie place because you have a different AOA at each speed to get the same lift number.

@foilstate is that 2.5% thickness to chord a typo for the wings? should definately be higher unless the game changer is 3mm thick?

Select to expand quote

TooMuchEpoxy said..

foilstate said..

Pacey said..
Drag coefficients can use different area definitions. For example for a blunt body such as a car you might specify the drag coefficient in terms of projected frontal area.

for wing profiles, drag coefficients are typically based on the surface area of the wing, not the projected frontal area, as this way, the area term used is the same as the area used to calculate lift or induced drag.

see en.wikipedia.org/wiki/Drag_coefficient for confirmation of this:

'The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere wikimedia.org/api/rest_v1/media/math/render/svg/33f7b7f93f93e7ba7bebb97efbe88e181ce332e4 (note this is not the surface area = wikimedia.org/api/rest_v1/media/math/render/svg/b81fcce302776a01dc66fc186a1ce0a616b4d772).

For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed."

The calculation would be more accurate with a dedicated drag coefficient for each mast instead of assuming they have the same. The nasa foil sim allows to get the drag coefficient of the masts (0.024 and 0.029 at 10kts), but not the whole setup. In the equation D = V^2 * S * Cd, Cd is for the whole foil. Not sure how the coefficients of the front wing, stab and mast combine to get Cd ?

The front wing coeficient would be all over thie place because you have a different AOA at each speed to get the same lift number.

@foilstate is that 2.5% thickness to chord a typo for the wings? should definately be higher unless the game changer is 3mm thick?

Sorry I made a mistake there, thank you for spotting it! Updated the table, more drag from the front wing.
- Front wing ~Game changer 1260 : Thick/Chord ratio 13% (~2cm/15cm), Chord 0.5ft, Span 2.7ft, AR 5.4, 2cm thick

Weight of the rider does not have a big influence on drag difference. A lighter rider will have a bit more drag from the mast proportionally, as the front wing generates less drag to lift his weight.

Front wing size has some noticeable influence, the smaller/faster the front wing, the more the mast thickness is felt in the total drag.
- Front wing Kujira750 : Thick/Chord ratio 13%, Chord 0.4ft, Span 2.2ft, 1.8cm thick
- Front wing Kujira1440 : Thick/Chord ratio 13%, Chord 0.6ft, Span 3.5ft, 2.2cm thick

Any suggestion of other edge cases I could try?

This is all great! Love this info! Camber also takes it into some fascinating and places! I think the one things missing is stall/vent, understanding the space between when drag starts to increase rapidly on the top end and stall and vent occur on the bottom.

I think the other thing we need is some speed numbers of one riding "topping out" on different wings. Does that rider "top out" at a consistent lbf of drag force on different wings?

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foilstate said..
Front wing size has some noticeable influence, the smaller/faster the front wing, the more the mast thickness is felt in the total drag.
- Front wing Kujira750 : Thick/Chord ratio 13%, Chord 0.4ft, Span 2.2ft, 1.8cm thick
- Front wing Kujira1440 : Thick/Chord ratio 13%, Chord 0.6ft, Span 3.5ft, 2.2cm thick

Any suggestion of other edge cases I could try?

Does your drag figure include induced drag as well as profile drag? Induced drag will be proportionally high at low speeds when lift coefficients are high.

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Pacey said..
Does your drag figure include induced drag as well as profile drag? Induced drag will be proportionally high at low speeds when lift coefficients are high.

actually, ignore the above question, I can see that it does by the way the wing drag is high at both low and high speeds, with a minimum in the middle. The resulting drag differences look pretty plausible, well done

Played around with camber some. More camber results in better efficiency at lower speeds(higher angled of attacks). Running a scneairio based on the gofoil RS 1000 at 0 camber and 25mph i needed 1.4 deg AOA to get 224 lbs of lift and produced 23 lb of drag. Pushing the camber to 2.8, required an AOA of -1.6 and resulted in 17lbs of drag (6lbs saved).

To kind of bring this home with a hypothetical. Maybe i get some GPS data showing i'm pushing 25 MPH on my 1000 Sq cm setup. Using foil sim i know that my ideal camber is 2.8. I can measre wings before i buy them and figure out if its going to be more or less efficient. If i'm a foil designer i can design that camber into the wing to target it to a specific rider weight.

My take away here would be that a heavier rider, a smaller wing, or a lower target speed (all other variables being constant) is going to get more efficiency from more cambered front wings. Also, being able to accurately measure camber is super important to measuting a relative rear wing angle.

I just need to figure out how to measure camber in wings.

Select to expand quote

Pacey said..

foilstate said..
Front wing size has some noticeable influence, the smaller/faster the front wing, the more the mast thickness is felt in the total drag.
- Front wing Kujira750 : Thick/Chord ratio 13%, Chord 0.4ft, Span 2.2ft, 1.8cm thick
- Front wing Kujira1440 : Thick/Chord ratio 13%, Chord 0.6ft, Span 3.5ft, 2.2cm thick

Any suggestion of other edge cases I could try?

Does your drag figure include induced drag as well as profile drag? Induced drag will be proportionally high at low speeds when lift coefficients are high.

If you're a racer you'll tilt the board to windward and, to get the edge on opponents, possibly home in on the angle where induced drag on the mast is zero. Better off having all hydrodynamic lift allocated to the one asymmetric foil rather than split it between two orthogonal foils.

Camber is then mid line between the front and rear chord line. A symmetrical foil or zero camber is like a rear fin or your mast. As you add camber one side flattens out and the other gains curve, this is what creates Bernulli's lift principle. The zero camber can produce lift with AoA, where as camber can produce lift at zero AoA (or negative as you have seen).

Select to expand quote

Windgenuity said..



Camber is then mid line between the front and rear chord line. A symmetrical foil or zero camber is like a rear fin or your mast. As you add camber one side flattens out and the other gains curve, this is what creates Bernulli's lift principle. The zero camber can produce lift with AoA, where as camber can produce lift at zero AoA (or negative as you have seen).

Yeah, I understand what camber is, I was asking how to measure it. Like if someone handed me a wing, a straight edge, an angle gauge, and a set of calipers could produce the percent camber?

Select to expand quote

TooMuchEpoxy said..

Windgenuity said..



Camber is then mid line between the front and rear chord line. A symmetrical foil or zero camber is like a rear fin or your mast. As you add camber one side flattens out and the other gains curve, this is what creates Bernulli's lift principle. The zero camber can produce lift with AoA, where as camber can produce lift at zero AoA (or negative as you have seen).

Yeah, I understand what camber is, I was asking how to measure it. Like if someone handed me a wing, a straight edge, an angle gauge, and a set of calipers could produce the percent camber?

The camber line is just the curve described by the midpoint between the upper and lower surfaces of the aero foil, and the maximum camber is just the maximum distance between this curve and the chord line.

A while back, I extracted the foil section from my gofoil wings - this photo should show you how I did it. Pretty easy and fast. I ran the section through XFoil software to get the lift/drag curves. If you really want to be accurate, this is how you do it

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jondrums said..
A while back, I extracted the foil section from my gofoil wings - this photo should show you how I did it. Pretty easy and fast. I ran the section through XFoil software to get the lift/drag curves. If you really want to be accurate, this is how you do it

This is a great idea, I will try that when time allows. The tricky thing is that the foil section is evolving on the tips!

Select to expand quote

TooMuchEpoxy said..
Played around with camber some. More camber results in better efficiency at lower speeds(higher angled of attacks). Running a scneairio based on the gofoil RS 1000 at 0 camber and 25mph i needed 1.4 deg AOA to get 224 lbs of lift and produced 23 lb of drag. Pushing the camber to 2.8, required an AOA of -1.6 and resulted in 17lbs of drag (6lbs saved).

To kind of bring this home with a hypothetical. Maybe i get some GPS data showing i'm pushing 25 MPH on my 1000 Sq cm setup. Using foil sim i know that my ideal camber is 2.8. I can measre wings before i buy them and figure out if its going to be more or less efficient. If i'm a foil designer i can design that camber into the wing to target it to a specific rider weight.

My take away here would be that a heavier rider, a smaller wing, or a lower target speed (all other variables being constant) is going to get more efficiency from more cambered front wings. Also, being able to accurately measure camber is super important to measuting a relative rear wing angle.

I just need to figure out how to measure camber in wings.

I think the number of design variables is mind bogglingy huge.
Surface,Planform,AR,Sweep,Twist,Camber,Dihedral and more...
Many change depending on which cross section you are looking at.Camber can be huge at the root and zero at the tips for example.Same camber can have the max thickness very forward or rearward.
Add weird/brilliant design ideas like winglets,steps or tubercles to further muddle things up.

So i would be a bit wary of conclusions reached from measuring camber ,or even getting a perfect cross section of the foil at a given point in the span.

You would have to accurately model the whole thingy and then run it through the software.Which is what the designer has done, maybe to find that the protos ride like crap because the even the best software modelling has limitations.

Select to expand quote

mcrt said..

TooMuchEpoxy said..
Played around with camber some. More camber results in better efficiency at lower speeds(higher angled of attacks). Running a scneairio based on the gofoil RS 1000 at 0 camber and 25mph i needed 1.4 deg AOA to get 224 lbs of lift and produced 23 lb of drag. Pushing the camber to 2.8, required an AOA of -1.6 and resulted in 17lbs of drag (6lbs saved).

To kind of bring this home with a hypothetical. Maybe i get some GPS data showing i'm pushing 25 MPH on my 1000 Sq cm setup. Using foil sim i know that my ideal camber is 2.8. I can measre wings before i buy them and figure out if its going to be more or less efficient. If i'm a foil designer i can design that camber into the wing to target it to a specific rider weight.

My take away here would be that a heavier rider, a smaller wing, or a lower target speed (all other variables being constant) is going to get more efficiency from more cambered front wings. Also, being able to accurately measure camber is super important to measuting a relative rear wing angle.

I just need to figure out how to measure camber in wings.

I think the number of design variables is mind bogglingy huge.
Surface,Planform,AR,Sweep,Twist,Camber,Dihedral and more...
Many change depending on which cross section you are looking at.Camber can be huge at the root and zero at the tips for example.Same camber can have the max thickness very forward or rearward.
Add weird/brilliant design ideas like winglets,steps or tubercles to further muddle things up.

So i would be a bit wary of conclusions reached from measuring camber ,or even getting a perfect cross section of the foil at a given point in the span.

You would have to accurately model the whole thingy and then run it through the software.Which is what the designer has done, maybe to find that the protos ride like crap because the even the best software modelling has limitations.

Anyone tried to precisely 3d scan a foil? Wondering if there is a cheap option out there. It would help to fairly compare shapes

Select to expand quote

foilstate said..

mcrt said..

TooMuchEpoxy said..
Played around with camber some. More camber results in better efficiency at lower speeds(higher angled of attacks). Running a scneairio based on the gofoil RS 1000 at 0 camber and 25mph i needed 1.4 deg AOA to get 224 lbs of lift and produced 23 lb of drag. Pushing the camber to 2.8, required an AOA of -1.6 and resulted in 17lbs of drag (6lbs saved).

To kind of bring this home with a hypothetical. Maybe i get some GPS data showing i'm pushing 25 MPH on my 1000 Sq cm setup. Using foil sim i know that my ideal camber is 2.8. I can measre wings before i buy them and figure out if its going to be more or less efficient. If i'm a foil designer i can design that camber into the wing to target it to a specific rider weight.

My take away here would be that a heavier rider, a smaller wing, or a lower target speed (all other variables being constant) is going to get more efficiency from more cambered front wings. Also, being able to accurately measure camber is super important to measuting a relative rear wing angle.

I just need to figure out how to measure camber in wings.

I think the number of design variables is mind bogglingy huge.
Surface,Planform,AR,Sweep,Twist,Camber,Dihedral and more...
Many change depending on which cross section you are looking at.Camber can be huge at the root and zero at the tips for example.Same camber can have the max thickness very forward or rearward.
Add weird/brilliant design ideas like winglets,steps or tubercles to further muddle things up.

So i would be a bit wary of conclusions reached from measuring camber ,or even getting a perfect cross section of the foil at a given point in the span.

You would have to accurately model the whole thingy and then run it through the software.Which is what the designer has done, maybe to find that the protos ride like crap because the even the best software modelling has limitations.

Anyone tried to precisely 3d scan a foil? Wondering if there is a cheap option out there. It would help to fairly compare shapes

That would be the way.
No idea about prices or precision etc...
With that and a 3d printed core maybe a DIY foil could be within my limited abilities :)

Edit: not that i plan on going down this rabbit hole,but this gizmo claims precision up to 0.1mm and price is around 600eur.
www.creality.com/es/goods-detail/creality-scanner-cr-scan-01

Even an Iphone12 can apparently scan with the right app, they have this built-in Lidar tech.There are also gizmos you plug into an IPad or Iphone and convert it into a scanner.Precision i do not know.

Reversed engineered the foil section of the game changer 1260 using jondrums technique. Accuracy is probably about 1mm, gives a rough idea of the profile. Maybe it would be possible to determine the naca digit from the foil section drawing? Will also give a go at the kujiras..

It is very likely not a standard NACA foil but a custom shape optimized for what they wanted to achieve. They may have started with a NACA and modified from there, but hard to say. Look up XFLR5 and you can do some analysis on the properties.www.xflr5.tech/xflr5.htm

Assuming 60cm of mast in the water, 2mm of thickness should change the glide at 10-16mph about the same as 2-3% change in front wing span would. I assume 60cm as that's about how deep the bottom of a pump is.

These numbers aren't very accurate as they don't account for surface interaction. My experience on different masts felt more significant than these numbers, I wouldn't be surprised if drag in reality is double this. Not sure how to calculate that though

Thanks for your input FoilAddict! What mast thickness do you think brands should aim for?
Current universal masts options are cedrus (bit draggy?), nolimitz (bit flexy?), armstrong+alchemy (bit flexy?). Is that a correct assumption? What's your current pick on the current masts market?

Strangely I found no perceptible difference in my real world use between the Axis 90cm 19mm mast and the 86cm carbon at +/- 14mm after a year of use. Wouldn't be the first time I've been accused of being insensitive though

Does the depth of the water change the amount of drag?
A little off topic but in the same realm. Putting the additional longer mast drag aside... Would a foil at 90cm depth have more resistance to flying (taking off) than the same foil at 60cm depth?

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Fishdude said..
Does the depth of the water change the amount of drag?
A little off topic but in the same realm. Putting the additional longer mast drag aside... Would a foil at 90cm depth have more resistance to flying (taking off) than the same foil at 60cm depth?

James Casey and Dave Kalama are using shorter masts in downwinds to make paddling up easier.

Slingshot carbon mast is incredible. Thinner at the bottom than any mast out there and very stiff. The Ono Foil mast is one of the best I've used, and is only 16mm thick so pretty fast. I liked my ride on the nolimitz, and the Armstrong is alright but could be a touch stiffer for big boards. Lift is too flexible for me.

the carbon used in a mast makes a huge difference, some race foil and prototype masts using nicer carbon are thinner AND stiffer than what we're riding now. Those masts would probably retail $2000+ though.

universal masts are the future, I would love to see a tapered one!
I find I notice the mast thickness drag most while pumping, and least while winging.
A longer mast probably isn't harder to takeoff because of the drag, it's more a combination of the foil's leverage in your board and how close the foil is to the surface power. Long masts tend to pitch up harder on takeoff, short masts take off very level. We tested this a while back with 2 identical setups on axis 930. One with a 70cm aluminum mast and one with an 85cm. SUP downwind I could get up in a few strokes on the short mast and a few minutes on the long mast. Almost exactly the same board, same fuse, front wing, tail, and track placement.

Select to expand quote

Hdip said..

Fishdude said..
Does the depth of the water change the amount of drag?
A little off topic but in the same realm. Putting the additional longer mast drag aside... Would a foil at 90cm depth have more resistance to flying (taking off) than the same foil at 60cm depth?

James Casey and Dave Kalama are using shorter masts in downwinds to make paddling up easier.

Yeah, I see that, and others have said this too. My question WHY does a shorter mast make for earlier take off?
Is their earlier flying ONLY due to having 50% less mast in the water at take off? (60cm vs 90cm mast). Or does the foil being 30cm deeper,(under more pressure) also add more resistance to moving through water?