VMG - formula and expanations for a study

[dave_gibsea]

Hi,

Long story but my daughter is doing a dissertaion for Uni on yacht racing and she needs a clear explanation and the formula for VMG with ideally some worked examples. There is one on wiki but it doesn't give actual numbers. She has been told that this is covered in one of the RYA Yachmaster publications but the problem is which one?

Can anybody advise on the this and/or point us to the book we need to buy?

Thanks,

Dave

 

[jac]

It is in the shorebased course notes - Mine are over 10 years old so may have been replaced but it has only 1/4 of an A5 page on it with a simple diagram. No worked examples but isn't it just the cosign of the difference between heading and bearing to waypoint x speed. ( ignoring tide for the sake of simplicity)

 

[lw395]

VMG can mean several things.
In racing, it is often upwind (or downwind) component of speed through the water.
On a GPS it may mean the rate at which the distance to WP is decreasing.

These are not the same thing unless you are dead downwind of the mark.
One is a good measure of sail trim.
The other is a measure of progress toward the mark.

Then there are subtleties, do you use the instantaneous wind direction or the average? Which is more useful varies between a short circuit dinghy race vs offshore.
Do you include tide?

 

[[70521]]

It is the speed (VOG) that you are approaching a point on the planet.

So if you are approaching the point in a straight line at 5kts your VMG is 5kts.

If you are approaching the point in a number of zig zigs your VMG might be 1kt. This would be much better as a diagram.

 

[johnalison]

No worked examples but isn't it just the cosine of the difference between heading and bearing to waypoint x speed. ( ignoring tide for the sake of simplicity)

With the small correction above, yes. VMG to wind will give the speed towards the apparent wind derived from the speed through the water, while VMG to waypoint will give the speed towards your destination derived from the SOG. My Raymarine instruments rather confusingly use the same term for both.

 

[pagoda]

It is the speed (VOG) that you are approaching a point on the planet.

So if you are approaching the point in a straight line at 5kts your VMG is 5kts.

If you are approaching the point in a number of zig zigs your VMG might be 1kt. This would be much better as a diagram.

Just think back to School/Uni.. it's nothing more complex than vector addition, and can be solved successfully by diagrams on paper if need be, without maths intruding..

 

[jimbaerselman]

VMG - the rate at which the distance to a given point decreases per unit of time.

It depends on the Cosine of the angle between Track over Ground (ToG) and bearing of the given point. Multiply that by the speed over the ground . . .

 

[BelleSerene]

As others have said, it's just trig.

Whatever she does, tell your daughter not to read the chaotic article on the topic in this month's Sailing Today magazine.

Here's a reasonable explanation - which ST appears to have 'borrowed' from to create its less clear article:
http://www.oceansail.co.uk/Articles/VMGArticle.html

 

[RupertW]

I agree with lw395 it can mean two different things - both solved with similar trig.

VMG on my old Raymarine was velocity to windward through the water, using only the wind direction log of speed through the water to work it out. So it tells you how well you are beating regardless of where your destination is or what the tide is doing.

VMG as I'd usually use it is the GPS progress over the ground towards your waypoint which is the same trig but against the waypoint bearing rather than wind direction, and speed from the GPS, not the log. So it tells you nothing at all about how well you are sailing but everything about your progress, tide helped or hindered, towards your destination.

 

[lw395]

As others have said, it's just trig.

Whatever she does, tell your daughter not to read the chaotic article on the topic in this month's Sailing Today magazine.

Here's a reasonable explanation - which ST appears to have 'borrowed' from to create its less clear article:
http://www.oceansail.co.uk/Articles/VMGArticle.html

That article is fine for explaining VMG towards an arbitrary waypoint, but the bit further down about VMG when sailing to windward is a bit woolly IMHO.
If the Ailing Toady article is worse....

Think about this.
A boat beating efficiently to windward, pointing 45 degrees from the true wind is sailing on starboard, starting off dead downwind from the mark.
It starts off sailing at 6 knots, it is making 6 cos 45deg, or 4.24 knots to windward and thus towards the mark
As it progresses, its vmg to windward stays the same, but the angle to the mark changes and its VMG to the mark falls.
Eventually, when the mark is abeam, the VMG to the mark has fallen to zero. But the VMG to windward has not changed.
It then tacks and the vmg to windward is the same on the other tack, but the vmg to the mark is 6 knots.

So how useful is vmg to the mark on a beat? Not very.
On a reach it will encourage you to initially sail for speed until you have to sail close hauled for the last bit.

Add in a bit of tide, a few windshifts and imperfect calibration of your instruments and what have you got?

It's also a time-lagged indication of performance, you can always boost the indicated VMG to windward by heading up. Until the boat slows down that is...

 

[johnalison]

I have both VMGs available and don't use either very often, mainly because a lot of concentration is needed to sail to it when beating. It is necessary to watch the VMG, the boat speed, wind direction and the sails, as well as occasionally looking where I am going. It can be useful when making adjustments to trim, and also for teaching purposes.

The only time I have found it useful to use VMG to waypoint was when beating north out of the Little Russell with the tide running at 3-4kn under us. The meter gave me a good indication of when I was reaching the edge of the strong tidal stream and thus when to tack.

 

[Buck Turgidson]

That article is fine for explaining VMG towards an arbitrary waypoint, but the bit further down about VMG when sailing to windward is a bit woolly IMHO.
If the Ailing Toady article is worse....

Think about this.
A boat beating efficiently to windward, pointing 45 degrees from the true wind is sailing on starboard, starting off dead downwind from the mark.
It starts off sailing at 6 knots, it is making 6 cos 45deg, or 4.24 knots to windward and thus towards the mark
As it progresses, its vmg to windward stays the same, but the angle to the mark changes and its VMG to the mark falls.
Eventually, when the mark is abeam, the VMG to the mark has fallen to zero. But the VMG to windward has not changed.
It then tacks and the vmg to windward is the same on the other tack, but the vmg to the mark is 6 knots.

So how useful is vmg to the mark on a beat? Not very.
On a reach it will encourage you to initially sail for speed until you have to sail close hauled for the last bit.

Add in a bit of tide, a few windshifts and imperfect calibration of your instruments and what have you got?

It's also a time-lagged indication of performance, you can always boost the indicated VMG to windward by heading up. Until the boat slows down that is...

can you expand on this please?
The reason I ask is that it would appear to me that you described the optimum way to get to the waypoint using VMG to the mark as the trigger to tack.

 

[johnalison]

The VMG won't give you a clear answer about when to tack, since the indicated speed will slowly drop off, and unless you can calculate what the VMG would be on the other tack precisely, you will still just be guessing. If you intend to make only one tack, you wiull need to know your CMG on the new tack (which may be possible, if it is likely to be the same as when you were previously on that tack) and then tack when the observed bearing to the mark is the same.

 

[lpdsn]

Hi,

Long story but my daughter is doing a dissertaion for Uni on yacht racing and she needs a clear explanation and the formula for VMG with ideally some worked examples. There is one on wiki but it doesn't give actual numbers. She has been told that this is covered in one of the RYA Yachmaster publications but the problem is which one?

Can anybody advise on the this and/or point us to the book we need to buy?

Thanks,

Dave

As it is racing, it is going to be about upwind and downwind VMG towards a mark. Polar diagrams are available for most yachts for a range of windspeeds, which cover off the optimum angles upwind and downwind. See also the North Sails books "Trim" and "Tactics" which cover the subject in a fair amount of detail without at all getting technical. Any textbook on yacht aero-hydrodynamic or even serious racing tactics (e.g. Frank Bethwaite or Stuart Walker) will provide a lot more mathematically based information.

I wouldn't expect the RYA to cover more than the bare basics. Efficient sailing is actually quite a small part of the RYA syllabus.

 

[Alan ashore]

Nobody's mentioned the value of VMG in an arbitrary direction. Sometimes described as VMC (V Made Good on Course). I have been known to enter very distant waypoints (One or other of the Poles is an occasionally useful special case) to facilitate monitoring this.

 

[lpdsn]

Nobody's mentioned the value of VMG in an arbitrary direction. Sometimes described as VMC (V Made Good on Course). I have been known to enter very distant waypoints (One or other of the Poles is an occasionally useful special case) to facilitate monitoring this.

At times I've been known to be a bit dissatisfied with where the race committe put the (first) windward mark, but I've never encountered one at the North Pole yet.

 

[Buck Turgidson]

The VMG won't give you a clear answer about when to tack, since the indicated speed will slowly drop off, and unless you can calculate what the VMG would be on the other tack precisely, you will still just be guessing. If you intend to make only one tack, you wiull need to know your CMG on the new tack (which may be possible, if it is likely to be the same as when you were previously on that tack) and then tack when the observed bearing to the mark is the same.

Assuming the tide remains constant won't it cancel itself out on the two tacks? (assuming we started dead downwind) The point at which VMG to the mark becomes (theoretically) zero is when the cog is at the tangent. The range from the mark will depend on the tide.

 

[johnalison]

Assuming the tide remains constant won't it cancel itself out on the two tacks? (assuming we started dead downwind) The point at which VMG to the mark becomes (theoretically) zero is when the cog is at the tangent. The range from the mark will depend on the tide.

The COG will become zero when you are on a course 90 degrees to the bearing to the mark. With the variation in boat speed in normal sailing, say 1/2 knot, the point won't be exact, and your boat may do better or worse than the 90 degrees. On the other hand, it won't cost you anything to try.

 

[pagoda]

At times I've been known to be a bit dissatisfied with where the race committe put the (first) windward mark, but I've never encountered one at the North Pole yet.

That's some windward mark!
I would often be more interested in how much extra distance i have consumed beating to windward than the reduced velocity vector in the desired direction. Both tell other parts of the same story!

 

[lw395]

can you expand on this please?
The reason I ask is that it would appear to me that you described the optimum way to get to the waypoint using VMG to the mark as the trigger to tack.

Much simpler to sort out what CMG you can make on the other tack, and tack when the mark is on that BRG.
Depending on wind or sea state, my boat will tack through anything from 75 to 95 degrees.

I race dinghies, and use a tacktick digital compass.
I mostly tack on shifts or in response to situations with other boats, the wind is rarely constant enough to calculate banging the corners of the beat exactly.
Also where I race, the tide is rarely constant across the course.