Toby P
01-13-2006, 07:04 AM
For displacement vessels hull speed is usually given as:
p * LWL^0.5
where traditonally p = 1.34 has been used as it matches the bow wave length to LWL.
Realising that it is not a constant value, David Gerr has derived an empirical formula for calculating p based on the displacement/length ratio (his book is on its way from Amazon, thanks Skippy!), which presumably is a more accurate indication of true hull speed. Clearly, however, hull form also affects a boat's maximum hull speed.
My thinking is that a formula along the lines of the one below could be used to establish whether a hull is limited to a hull speed or whether it is able to break free and continue accelerating in displacement mode e.g. catamarans.
k = (D:L* tan(a))/(L/B)
D:L is the displacement:length ratio (non dimensional),
a is the bow angle of entry,
L is waterline length,
B is waterline max beam.
The waterplane coefficient, Cw, could be used in place of angle of entry of bow, ideally just Cw of forward half of hull would be used.
Some critical value of k splits those hulls that can readily progress through the normal p = 1.3 - 1.5 barrier e.g. cats, from those that can't. Some coefficients and indices need to be added to the terms in this equation to ensure that the influence of each factor is weighted properly.
For hulls that do not exceed the critical k value, factors other than bow wave formation dominate drag, so the concept of relating the hull's maximum speed to the square root of its length is of little practical importance. However, for hulls that do exceed the critical k value the hull speed coefficient, p, could be estimated on a revised Gerr formula that incorporates coefficients of form such as L/B, D:L and a. Has anyone done this? Does it sound like a stupid idea?
Alternatively you could take the opinion that there is no such thing as hull speed, hence trying to calculate it is pointless. Whilst this is technically correct (supply enough power and you WILL go faster) I believe that the notion of hull speed has proven it's worth over the years, so trying to establish it more accurately (without the need for CFD/VPP software) has to be a worth while exercise.
P.S. For the background to this thread see Humpless Planing in the Sailboat section of this forum.
p * LWL^0.5
where traditonally p = 1.34 has been used as it matches the bow wave length to LWL.
Realising that it is not a constant value, David Gerr has derived an empirical formula for calculating p based on the displacement/length ratio (his book is on its way from Amazon, thanks Skippy!), which presumably is a more accurate indication of true hull speed. Clearly, however, hull form also affects a boat's maximum hull speed.
My thinking is that a formula along the lines of the one below could be used to establish whether a hull is limited to a hull speed or whether it is able to break free and continue accelerating in displacement mode e.g. catamarans.
k = (D:L* tan(a))/(L/B)
D:L is the displacement:length ratio (non dimensional),
a is the bow angle of entry,
L is waterline length,
B is waterline max beam.
The waterplane coefficient, Cw, could be used in place of angle of entry of bow, ideally just Cw of forward half of hull would be used.
Some critical value of k splits those hulls that can readily progress through the normal p = 1.3 - 1.5 barrier e.g. cats, from those that can't. Some coefficients and indices need to be added to the terms in this equation to ensure that the influence of each factor is weighted properly.
For hulls that do not exceed the critical k value, factors other than bow wave formation dominate drag, so the concept of relating the hull's maximum speed to the square root of its length is of little practical importance. However, for hulls that do exceed the critical k value the hull speed coefficient, p, could be estimated on a revised Gerr formula that incorporates coefficients of form such as L/B, D:L and a. Has anyone done this? Does it sound like a stupid idea?
Alternatively you could take the opinion that there is no such thing as hull speed, hence trying to calculate it is pointless. Whilst this is technically correct (supply enough power and you WILL go faster) I believe that the notion of hull speed has proven it's worth over the years, so trying to establish it more accurately (without the need for CFD/VPP software) has to be a worth while exercise.
P.S. For the background to this thread see Humpless Planing in the Sailboat section of this forum.