Motor or tack for cheap beer?

[concentrik]

I posted about this a little while back but didn't get much response - probably because it's of little interest! - but ended up working it out for myself anyway because I'm bored waiting to return to the boat; here's what I found.

I want to get to Port Cockaigne for happy hour at the marina bar but drat! there's 12kn of wind right on the nose and I've got 20 miles to do. Burning diesel makes the drinks dearer, but I really don't want to miss out on their fantastic Cirriana cocktails.... motor or sail?

My OpenCPN chartplotter is encouraging when I tack off*, telling me about my Velocity Made Good (doing 6kn now instead of 4kn under engine) and Time To Go (I'll be there when they open!), but after a while I get a bit suspicious as I seem to be slowing down according to the VMG reading. And the TTG seems to be on a different time zone.

Luckily our recently-joined crewmember has 'O' level maths (I don't - no surprise there) and puts me right on a couple of things:

VMG is virtually useless on a tack since it treats tacking as a crosstrack error. This makes the TTG or ETA flawed.

It's mainly down to the boat's tacking angle whether I'll be enjoying a cool drink at all.

Even more lucky, the trig wizz with the 'O' level quickly puts together a tiny Excel spreadsheet which clearly shows that I was hopelessly optimistic and that my boat is rubbish upwind. By now, even if I put the engine on and power directly to the bar I'll be paying full price.

You can try it yourself here (you need to download and run it in Excel or similar):

https://www.dropbox.com/s/cl24czpja3afvic/Tack or not.xlsx

* I know I could lay a new course on the chartplotter to incorporate the tacks I plan to make and the ETA and VMG would read fairly true. The foregoing is just a bit of fun - but sobering nonetheless! VMG and ETA only work if you're right on the line.... but you all probably knew that anyway.

 

[neilf39]

Assuming wind on the nose and no currents and boat all nicely set up so tacks are symmetrical then it is just a case of working out a triangle based on a line from you to the destination and the best angle you think you can make. In 12kn in my elderly boat I would allow for 40 degrees plus 3 degrees leeway. If I can sail at 6Kn at that angle then my VMG to destination is 6 x Cos (43 degrees) so 4.39Kn or being generous 4.4kn, allowing for bad steering, time lost in tacks make it 4Kn so whether you sail or motor makes little difference. You may as well sail and save diesel and cash if motoring speed is 4Kn. Its a 5 hour trip either way.

In normal cases you will have current and wind at varying angles at different times which is why you go through the rigmarole of plotting all this when passage planning.

I don't know how clever openCPN is and whether you can programme in tacking plus angles etc etc. and how it decides how to tack to get there. Does it take converging lines to tack between so you do an ever increasing number of shorter tacks for instance.

 

[concentrik]

Assuming wind on the nose and no currents and boat all nicely set up so tacks are symmetrical then it is just a case of working out a triangle based on a line from you to the destination and the best angle you think you can make. In 12kn in my elderly boat I would allow for 40 degrees plus 3 degrees leeway.

Is that 43 degrees off the rhumb line or 43 degrees tacking angle?

 

[Twister_Ken]

Is that 43 degrees off the rhumb line or 43 degrees tacking angle?

I think a 43º tacking angle would bring home the America's Cup.

 

[concentrik]

I think a 43º tacking angle would bring home the America's Cup.

Yes that's what I thought, just giving nielf the benefit...!

But a 43 degree course to windward will make the overall trip over 30 miles rather than a direct 20, even assuming his tack angle is (an optimistic) 100 degrees. His speed would need to be 6.18 kn, without allowing for any mistakes. So I think sail or motor does make a huge difference, sail is 50% slower. Will somebody please check my maths??

View attachment 44313

 

[neilf39]

OK meant 86 degree tacking angle. If motoring or sailing was the same speed then yes it is 50% further but the op said motor at 4kn or sail at 6kn and the answer is about the same. Surprised you think 100 degrees is an optimistic tacking angle. I can get 80 close hauled but leeway will add 3 to 5 so I reckon I get just under 45 off the wind as my relative direction of travel if no current.

 

[charles_reed]

The secret lies in the sea-state. If it's smooth and there's no contrary current, you'll probably do best motoring directly to windward, but there'd be little to choose in MGW. However, as the sea gets up you have to power up the boat more and the tacking angles get wider and wider.
Personally, I do neither but motor-sail under main alone - that becomes impossible in above a seastate 6 - at which point I choose my downwind target.
Under main, I can get appreciable drive with a tacking angle of 60-80 degrees (again depends on seastate) and make 6 knots when at the same rpm going directly to windward I'd be only getting about 4.1.
My boat, however, has a big fully battened main on a 3/4rig and a Brunton Autoprop.