Ferry Angle Calculations - Beginner Level

[...]

Ferry Angle Calculations – Beginner Level

One the great values of NSPN is the ability to tap into the combined knowledge of so many highly skills paddlers. This thread is my attempt to mine knowledge in preparation for our seminar later this month with the Grand Poobah of Navigation, John Huth.

In preparation for paddling in Alaska, I have begun reviewing navigation risks, current flows, distances etc. One potential section of travel as outlined on NOAA nautical chart 16708 involving crossing Valdez Narrows from the radar tower at Potato Point to the northern edge of Jack Bay. A high consequence crossing that is 3 miles in length. The crossing is planned for approximately 8:30AM on the morning of July 9, 2014.

My task is to calculate the heading for the team as read off the deck compass and determine the approximate time of arrival at the entrance to Jack Bay.

To aid me in this task, I have assembled the following tools and data:
1. NOAA Nautical Chart 616708, which depicts topographical land mass, in a chart case.
2. Waterproof watch.
3. Deck Compass.
4. Listo pen
5. Access to the Valdez Narrows current station data for July 9, 2014. That data includes current speed of +0.5kn and 34 degree direction at approximately 8:30AM.
6. Team paddling speed of 3 knots.

In an effort to keep this example at the beginner level, I am assuming the following:
1. We will encounter no significant wind speed or waves as added variables.
2. Our crossing will involve a beam current for the duration.

With the data and known variables above, I will use the following formula:
Current Speed (0.5) divided by Paddling Speed (3) times 60 degrees equals Ferry Angle (round to 10 degrees).

To arrive at my deck compass heading, I determine the heading on my chart using a hand held compass (110 degrees) and subtract the variation (20 degrees) then add ten degrees to compensate for the flood current for a heading of 120 degrees.

To determine the time of arrival at Jack Bay, I use a value (taken off a commonly available published table) that states a 15 degree ferry angle or less, crossing speed will be at 100% of normal speed. Therefore, I should arrive at Jack Bay at approximately 9:30AM.

Now, let’s determine if this process documented above is sound or does it have more holes than a slice of Swiss cheese!

Warren

Edited January 4, 2014 by Warren

[leong]

Hi Warren,

You first stated that the direction of current is 34 degrees (I assume that’s respect to true North). Then in your simplification, you stated “Our crossing will involve a beam current for the duration.” But since your intended course over ground (COG) is 90 degrees (110 – 20), the current is not perpendicular to your COG. If your simplification is purposely disregarding the 34 degree current then your calculations appear to be correct (at least to within the approximation formula that you used).

But if you want to correctly use the 34-degree current than you need to do some additional calculations:
1. compute the perpendicular component of the current to your intended COG
2. compute the component of current parallel to your intended COG

I’ll leave out the rest pending any response.

-Leon
PS
Note 1. Not part of your exercise, but John Winters (the famous small boat designer) argues against using ferry angles. He claims that the pursuit curve (always aiming your bow towards the target) is more efficient (see this and this).

Note 2. A GPS can always keep you on the correct COG, no matter how the wind or current velocities vary over time. I don’t think that Winters would disagree with me that this is the most efficient way to cross from point A to point B. Perhaps I’ll ask him via email.

Note 3. John Huth has an Excel program that does the ferry angle calculations for the general case.

[EEL]

Warren:

At the risk of sounding irresponsible or reckless, in stable weather given amount of current and distance of crossing I would tend to make a simple SWAG for ferry angle using the shortcuts you mention just in case fog rolled in, then find a decent range with a reasonable set off, and just go for it. The ferry angle in this case is just not big enough to worry about all that much if you are trying to hit a shore as opposed to a small island even if fog rolls in. Of course perhaps I just to not realize the complexity of the endeavor.

Ed Lawson

[...]

Leon,

You are correct that my reference to the direction of the flood at 34 degrees was not intended to demonstrate a true beam current. But you noted a very important point in your first line. I have always assumed the published data for the direction of the current as determined from the current reference stations was stated as magnetic north. I located my copy of "Captn. Jack's Tide and Current Almanac" and it states very clearly on page 6 how the direction is expressed in true north. Great discovery! Thank you!

I do agree with John Winters that a pursuit curve is a more practial approach as long as you have visability. Also, a good GPS can help.

I do, however, see value in understanding the basics regarding ferry angle calculations and to run the numbers prior to launch. This realization hit home this past summer while paddling the San Juan Islands. There the max current is typically in the 2.4 to 2.7 knot range as you paddle from Patos, Sucia and Matia. On one day of the trip, our team witnessed a trained guide with 3 paid clients unable to make his intended journey due to a lack of understanding the current speed and direction. That day he was fortunate to be able to arrive on Matia for the night. Had the wind picked up, it could have been a very unpleasent situation. At times, what the water is doing under me can be as helpful as what the clouds are doing over me as I seek to identify my risks.

I would value seeing John's Excel program! Perhaps it can be used for bow and quarter currents as well?

Warren

[...]

Ed,

You are correct, the current speed in this example is too slow to warrant a high level of concern. This example, however, is a pending real life situation.

I like to explore new waters and I like to identify risks and develop solutions. Until I began looking at the current reference station data, I had no idea what the currents were doing in that section of Prince William Sound. Ferry angle calculations just seem to me to be another tool in my navigation tool kit. But as you noted above, there is value in understanding a short cut approach to making a ferry angle adjustment when warranted. Of course, knowing me I would probably just break out my GPS. But I do need to practice ferry angle calculations!

Warren

Edited January 4, 2014 by Warren

[EEL]

Warren:

A few random thoughts. After looking at chart I take it you are leaving around area of Green 11A and crossing the shipping channel with VTS noted. So I would be sure to check about that. As noted, NOAA tide current charts always show current in "true" degrees as in with respect to true north. Given short crossing and starting at or near max, the variation is current speed over crossing would not be large due to time. If you started at other times in the tide cycle then the variation over the crossing would be greater due to time. For example, starting at the start of the second hour would mean the current would go from 50% to 90% during crossing. Also the velocity of the current will not be constant during crossing since the velocity depends upon location and your location is constantly changing. Crossing a strait as this proposed one appears to be might even involve starting and ending in an eddy which adds another layer of complexity.

I totally agree that knowing how to SWAG ferry angles using the shortcuts you describe is important. I also believe a good idea to at least have some understanding of how to use vectors as well and , more important, do as you are by plotting at home, taking notes, and having the notes with you. I was pointing out that in some circumstances a quick and dirty approach might be just as effective. Often you can just use your fingers to measure distance and to determine a course from a chart while paddling and do so with adequate accuracy.

It is easy to underestimate the impact of current , but even a .5Kt. current represents 18% of typical paddling speed.

You said you used the handheld compass with the chart to determine course. Did you simply use the compass as a protractor with the true north grid on the chart (great use BTW) or were you orienting the chart using the compass as we tend to do on land when hiking?

For home planning I find a marine protractor quite handy when dealing with paper charts. Must say I often use electronic plotting tools, but something about looking a paper charts during the winter appeals to my old fashioned mind...or is it just old mind..I forget.

Ed Lawson

[...]

Ed,

Yes, there is something nice about laying out large NOAA paper charts while holding a cup of hot cocoa and the outside temperature reading -4 degrees. For me, the nautical charts are one of my main safety tools. I need to become very familiar with all aspects prior to a journey. During the San Juan Island trip I purchased a nautical chart which did not have any topographical land mass notations. It was a major handicap as I attempted constant range adjustments with a team that was local to Pudget Sound and all had the proper charts. I will not make that mistake again.

And yes, I am talking about making the crossing at Green 11A. By the way, the topographical section of my chart shows an area labelled "LT OBSC" around Red 12 at Entrance Point on the northern side of Jack Bay. It is obvious that the light is obscurred due to the land formation. (As an aside, I could not locate the meaning in my Chart No.1 book. Perhaps it is too obvious to list in the Lights section.) Here is yet another way in which the chart needs to have the topographical land masses.

Warren

[JohnHuth]

Warren -

OK, I tried to do this as a paper exercise. The first thing that came up was that I saw the crossing as 1.3 nm, not 3. I'm attaching a jpeg of the chart I used, including the scale at the bottom.

The solid line is my assumed course. Normally, I'd probably make a deliberate compass error to hit the other side of the strait to the north of the path indicated, just in case fog rolled in, so I don't blunder into the reaches of Jack Bay and wonder what happened. But in this case, I just eye-balled the most direct route.

I'm attaching my spreadsheet for current calculations.

Comments - although the speed doesn't change a lot, even 0.5 its causes some change in heading - something like 9 degrees - not a huge amount, but something to be aware of.

I got a magnetic heading of 98 degrees. On the jpeg, I drew in magnetic lines spaced by 1 nm.

I got a crossing time of 25 min at a speed of 3.1 kts, so arrival at 8:55.

Biggest issue is the difference between my estimate of distance and yours. I used chart 16707, not 16708.

John H.

Ferry angle.xlsx

[...]

John,

You are correct on the distance. The chart I am using does not have a scale, so I referred to the Lat/Long scales around the edge and mistakenly read the wrong scale. (My chart (16708) has a scale of 1 : 80,000. I can see where your chart has a scale of 1 :40,000.)

You have touched upon a very important aspect of navigation which we have encounter first hand. The need for two paddlers to attempt the calculations independent of one another and then compare results. I suspect it is not uncommon to have mistakes made. Or in my case, dopey mistakes made! Perhaps the gentle readers of this thread will see how this example can drive home the need for paddling teams with more than one navigator on board.

John, thank you for your work on this topic! I look forward to attending your seminar later this month!

Warren

[JohnHuth]

Hi, Warren -

I'll talk about one approach I use - it's a way of preparing charts somewhat like what I have in my posting.

There are a couple of issues that can be confusing and can waste time on the water. Typically when the chart is folded up to the section you want to see, the scale is often hidden - so I draw magnetic lines spaced by 1 nm throughout the chart.

This helps in two ways - one is that you have a handy scale to use - use the little lanyard in the hand-held compass to look at a course, and then stretch it perpendicular to the lines in the chart to estimate distances. The lines drawn with magnetic declination in means that you can steer magnetic and not have to hassle with a lot of addition and subtraction, trying to remember rules like "east is least".

Now, this is not always advised by instructors. I was on a course led by Shawna Franklin who was a "east is least" fan, and she also took exception to my drawing magnetic declination lines on the chart saying "I don't have the time to show up in a new town, purchase a chart and draw in magnetic lines like that." Well, I'd actually done just that the night before.

I've found that a simple, visual approach reduces the chances of error and provides a kind of intuitive feedback.

The link below is an article about a guy who was crossing Nova Scotia and used a declination of 18 deg. east rather than west and got lost in the process:

https://static.squarespace.com/static/503d2a37e4b0344ab347611e/t/50491384e4b0960a81cd4c82/1346966404307/

Anyway, I'll go over this in the course.

Best,

John H.

[John Martinsen]

From my experience in Prince William Sound it's a fairly benign place to paddle in the summer, other than the rain and a light bit of traffic. I don't remember currents being a huge issue, other than in obvious places with constrictions, like Culross passage, but nothing like you would experience in the San Juans. Not to say there isn't something to be gained from the preparation and practice with that type of tool and what not, or that there isn't a little current here and there, but it's nothing you can't assess and deal with as you go. So here's my take on crossings. I like to try and keep things simple so I can focus on my paddling, not have to fuss and look at the deck to constantly check a GPS or chart, but instead have my kayak make a true course and clean crossing. I'm not the most technical navigator, I like to keep it simple and intuitive, but here are my recommended ingredients for a PWS crossing. Know where you want to start the crossing, once there, look over to where you want to cross to, pick an obvious landmark on the other side, point it out to your group so you have a common reference point to head to. As you leave shore look over your shoulder to check your back bearing, and adjust your angle as you go to compensate for wind\current if need be. Fairly simple. But it relies on strong piloting and chart reading skills, reinforcing position by terrain, landmarks, and range lines if possible. Also means doing a fair bit of homework the night before, having a solid compass bearing (preferably in magnetic north as John recommended) to help solidify my course (but only as a reinforcement to my line of sight) knowing the distance without having to think about it and therefore my travel time. Keep your eyes up. Find a good place to take a break before starting and once finished. I found on the west coast the scale of things would throw me off for a day or two until I could get my head around that, and the seeming reversal of magnetic north would take awhile to adjust to as well. Also a lack and or spreading out of nav-aids on the water takes away any cheats as in more populated areas. But I think paddling in the sound will offer you a chance to focus on a line of sight type crossing until it becomes comfortable, and John Hugh mentioned the word intuitive, which is something I aspire to in my navigating.

A good pair of binoculars are hugely helpful for "scouting" out the crossing before even leaving shore, as well as for assessing ocean state before leaving camp and or protected waters. Also great for all the amazing wildlife you're likely to see out there as well. Have fun, sounds like a great trip.

[...]

John M,

I very much enjoy reading about your insights into paddling Prince William Sound. Although I have a compact and light weight pair of binoculars, I had not thought about adding them to my gear list. Now they are in the kit!

I will admit I enjoy the preparation and planning phase of any adventure. So whether it is getting my head around ferry angle calculations for John's seminar adventure or preparing for an expedition on PWS they both present learning opportunities. For me, the more I invest in each, the more I will benefit from the knowledge transfer.

I hope you can attend John's seminar on navigation. I would enjoy meeting you and talking about Alaska.

Warren

[leong]

So here's my take on crossings. I like to try and keep things simple so I can focus on my paddling, not have to fuss and look at the deck to constantly check a GPS or chart,

In strong cross-winds/currents, I can't imagine anything simpler and/or less fuss than setting a GoTo-Waypoint on your GPS and paddling so the GPS's arrow is pointing to the top of the screen. I just glance at the arrow once every minute or so. I think it's a lot easier than keeping two features lined up (a range). Besides, sometimes there are no features to line up. I think paddling from the Isles of Shoals to Rye Harbor is a good example of "no ranges", especially in the dark or in a fog.

Nevertheless, one should practice with a chart and compass, learn to compute ferry angles, use ranges and other manual navigation techniques because a GPS can fail in many ways.

-Leon

Edited January 5, 2014 by leong

[...]

I wanted to circle back on the ferry angle thinking and mention one other variation to consider. Last summer I was a member of a paddling team which planned to paddle from Terrill Beach on the north side of Orcas Island to the south side of Patos Island, a distance of 5 miles. A direct route would put us on a heading of 315 degree magnetic. We would launch at 8:30AM. The current station had the speed at 2.4 knots, at 10 degrees magnetic at 9:38AM. The route would take us across the east end of President Channel and across the West Bank where there is a dramatic change in the water depth. We suspected the change in water depth could cause a shift in both speed and direction of the current over a distance of 2+miles. A mistake regarding our ferry angle calculations would sweep us into Rosario Strait and then into Boundary Pass which both have heavy freighter traffic.

We did, however, want to get to Patos at around 10:30AM. Instead of using our ferry angle approach directly from Terrill Beach to Patos Island, we paddled west along the shore of Orcas Island staying out of the east bound current until we arrived at Point Doughty for a distance of 2 miles. We then launched in a wide arc heading toward Patos while skirting the edge of West Bank for a distance of approximately 4.5 miles. Although the total distance was approximately 6.5 miles we arrived at around 10:15AM ahead of schedule.

That day I learned three important lessons:
1. You need a nautical chart that includes detailed water depths to help you estimate what the current might be doing along your route.
2. You need to have a plan prior to launch which includes a careful understanding of your risks.
3. Sometimes the best approach is not a direct route, frontal attack on the problem. Let the forces of nature help you so you have plenty of time for morning tea once you arrive at your destination.

Warren

[EEL]

"We suspected the change in water depth could cause a shift in both speed and direction of the current over a distance of 2+miles."

Warren:

To further help those reading perhaps answering these questions would be useful.

What was the nature of the depth change?
Was in shallower or deeper? Would the current speed increase or decrease and how is that related to whether the depth is more or less than at the current station location?

Why would the current direction change?

Ed Lawson

[PeterB]

Warren.

.

Is this just a fun winter practise / planning exercise, or is this an actual assignment you’ve been given ,as in: your group is actually planning a crossing between these points at or close to the exact time and date given? .If the former, fine, it ‘s a fun planning exercise focusing on angles, boat speed ,current , etc. .

If the later, more information is needed and the whole affair might be approached from a different perspective ; what is your general destination: are you traveling away from Valdez and down into Prince William sound or back from Prince William sound towards Valdez? E.G. As this is a shipping channel with occasional big vessels traveling at speeds of perhaps 12-15 kts, this ups the ante for crossings , so your crossing would want to be considered in a larger context; shipping channel,where you're going, etc.

[...]

Patos Island.pdf

Ed,

It is said a picture is worth a thousand words. Please find attached a picture of the waters in question. Notice the symbols of “A”, “B” and “C”. Originally the idea was to get from “A” to “B”, after calculating the proper ferry angle. Notice the depth of the water in the channel is greater than 350 feet and the depth of the water in West Bank is as little as 8 feet. There was also another concern at Parker Reef, just northeast of Terrill Beach. It is known for being hazardous to kayakers during max current. We would be in those waters at around max flood on purpose to test our skills.

I vividly remember dutifully running the numbers in an effort to determine proper ferry angle as well as the preferred boat speed to get to Patos Island without being sweep into the Parker Reef or Rosario Strait. At the time I lost sight of the need to run multiple options first and then select the one best suited to the team and the lowest risks.

We ended up paddling from “A” to “C” to “B” and enjoyed a hot cup of tea on Patos Island as planned.

Ed, I hope this helps answer your questions.

Warren

Edited January 5, 2014 by Warren

[...]

Peter,

You are absolutely correct that more information could have been stated. My goal was to find a fun activity. Did you enjoy it?

Warren

Edited January 5, 2014 by Warren

[PeterB]

So you picked a crossing for practice , and that was what you selected? But not as part of a larger plan, so it was a circumscribed crossing exercise.?

I very much enjoyed my look at the Prince William sound chart. It looks like an environment meant to be explored by kayak. Precisely why I asked whether this crossing was part of your actual plan; I think my approach to your crossing might be different depending on whether my group was coming or going from Valdez.

[...]

Peter,

Yes, Prince William Sound appears to be an amazing area to explore. My perference would be to spend time exploring both Columbia Bay and Glacier Island rather than Jack Bay. Jack Bay does appear to be amazing with multiple glaciers, but that area might be saved until an expanded exploration of the east end of PWS is planned. The trip I hope to complete will begin in Valdez and end in Whittier. Part of the logistics will involve taking the kayaks and all the gear on the high speed ferry, M/V Chenega, and travel from Whittier to Valdez at 11:30AM on July 7, 2014. The trip over to Valdez will give us an opportunity to see most of the waters we will be paddling over the following 12 days. I some ways, the logistics may be as amazing as the paddling. Take a look at the M/V Chenega on "YouTube"

Keep in mind the shift in the starting location from Whittier to Valdez is done by design since the prevaling winds during July would be out of the east. If the winds do pick up, they will simply push us along on our merry way!

Warren

Edited January 5, 2014 by Warren

[EEL]

Warren:

I asked the questions to generate a follow up discussion about when and why the speed of the current might be influenced by changes in depth of a channel. So not sure the picture answers or leads to the answers of the questions since the data is not there. However, the picture does explain why your guide picked the route you followed. When you first described it, I thought you had just followed the alternative of going upstream by a distance equal to the set and then paddling across and letting the current bring you down to the destination. My guess is he was doing something rather different based on solid local knowledge and good guiding practices. By going up stream he avoided having his party working against the current while ferrying across which may have been accelerating due to the narrowing channel and reduced their risk of being shoved down onto tide rips or worse if the party was weaker than expected or something nasty happened along the way. More interesting, if the arrows show tidal streams, then he was also going up stream to where the tidal stream split to flow around the shallows so that once you got aways off Pt. Doughty you would be in a tidal stream going in the right direction to carry you to your destination which perhaps explains why you got there in good time. A very nice bit of navigation.

Ed Lawson

[...]

Ed,

Yes, I had the benefit of tapping into Matt Nelson's local knowledge. He is a superb treacher/coach.

Sorry, I do not have the knowledge you seek regarding how a current is affected by a significant change in the ocean depth. I can tell you we did play in the shallow area while the max current was running. The waters were moving in different directions although not as fast as in the channel. Matt would point to the changing direction of the sea weed which was visable in the very shallow areas. A fascinating area to explore when accompanied by a guide like Matt.

Warren

Edited January 5, 2014 by Warren

[EEL]

Warren:

If you have "Kayaking Puget Sound and the San Juan Islands" there is a good discussion about tide rips and why currents accelerate. Good discussion of where and when to cross to Patos also. For example, doing so on the flood is recommended, and it appears that is when you were doing it. Again, sound navigation.

Ed Lawson

[leong]

To determine the time of arrival at Jack Bay, I use a value (taken off a commonly available published table) that states a 15 degree ferry angle or less, crossing speed will be at 100% of normal speed. Therefore, I should arrive at Jack Bay at approximately 9:30AM.

Funny that all the publications that I looked at provide a handy dandy approximation formula for the Ferry Angle (CrossCurrent Speed divided by Paddling Speed times 60 degrees). However, except for a table look-up approach and a hard to draw and compute (while on a kayak) answer based on a vector diagram, I couldn’t find a simple approximation formula for Speed Made Good (Crossing Speed when paddling with the ferry angle).

I had a little extra time so I derived such an approximation formula for this Speed Made Good. I think this is better than memorizing a lookup table or carrying one with you every time you go kayaking.

Define the reduced crossing speed (speed made good) to be 100X% of normal speed.

Then a very good approximation to X (much better than the tables or eyeballed vector diagrams) is

X ~ 1 - [(c/p)^2]/2, where c is the crosscurrent speed and p is the paddling speed.

I think that most smart phones could do this math (or buy a four-function calculator from a dollar store)

PS

For readers that are math oriented:

The exact formula is X = cos(arcsin(c/p)), where c is the cross-current speed and p is the normal paddling speed. Note arcsin(c/p) is the exact ferry angle in radians.

Approximating cos(arcsin(c/p)) with the first two terms of its Taylor Series we get

X ~ 1 - [(c/p)^2]/2.

Incidentally, I guess that the Ferry Angle approximation formula was derived like the following:

FA = arcsin(c/p) is the exact ferry angle formula

The first term of the Taylor Series for arcsin(c/p) is just c/p. However, the answer is in radians.

To convert to degrees multiply by 180 degrees/pi = 57.296 degrees. Then use 60 degrees as an easy to remember (and compute with) approximation of 57.296 degrees. Thus we have the approximation formula

FA ~ (c/p) 60 degrees.

Edited January 6, 2014 by leong

[JohnHuth]

The 'space' of possible paddling speeds, current speeds, and angles makes it tough to come up with any easy-to-remember way of taking care of all cases. However, what I keep in my head is the following: most folks paddle at about 3 kts. Most crossings of any consequence are at 90 degrees to the current. Using this - there's a fairly easy 10-20-30-40-50 rule that goes in increments of 0.5 kts

Current speed Correction angle

0.5 kts 10 degrees

1.0 20 degrees

1.5 30 degrees

2.0 42 (40) degrees

2.5 55 (50) degrees

The relation is pretty linear up to 2 kts of current, and then you can see the divergence set in. At 3 kts, there is no solution. But, the 10-20-30-40 rule works pretty well.

In some busy channels, i'll shoot right across if there's a lot of boat traffic, and let the current carry me, so I'm not in the channel as long. In some cases, if the winds blowing against the current and creating waves, I'll surf the waves, so that gravity is helping me fight the current. There are all kinds of exceptions to keep in mind.

OK, on the topic of channel depth - it's a tricky subject, but I'll take a whack at it. There are two figures below. The top one is just a tube that has a change in diameter. If there's a constant pressure difference between the two ends, the speed of flow in the wide diameter is lower, and when there's a constriction, the speed increases - this is how the volume of water passing through is a constant. This is called the 'continuity condition'.

So, imagine a V-shaped channel like the second figure. Take two snap-shots of the tide cycle - if the depth of the channel is about the same scale as the height of the tide, then this is relevant. When the tide is low, the area of the channel available for water to pass is constricted, so you'll get a higher speed of flow, when it's at a higher part of the tide, there's more cross-sectional area available for the flow and the speed drops. It depends, of course, on the shape of the channel and the height of the tide, but you get the idea.

I've seen exactly this happen at the cut on South Beach near the Monomoy's. At low tide, the current is appreciable, because the cut is pretty shallow, but at high tide, the current drops off appreciably.