A look at the GPS data from our 8-day 200-mile coastal cruise in June 2010.
Excellent trip reports about our June cruise with the Spartina are already available in a brief summary by SandyBottom (photo at left) and especially in The Log of the Spartina by Steve Earley (that's Spartina in the background in the photo at left.)
Steve has raised the enjoyment of small sailboat cruising to a fine art. He really knows how to savor the entire experience --from the anticipation and planning, to the adventure itself, to looking back with great photos and stories. Who knew even the planning stage could be so much fun?
This post provides a complementary look at (1) the ups-and-downs of sailing speed and (2) our first experience sailing with a motor on a multi-day cruise.
Motor or no motor?
Steve has raised the enjoyment of small sailboat cruising to a fine art. He really knows how to savor the entire experience --from the anticipation and planning, to the adventure itself, to looking back with great photos and stories. Who knew even the planning stage could be so much fun?
This post provides a complementary look at (1) the ups-and-downs of sailing speed and (2) our first experience sailing with a motor on a multi-day cruise.
Motor or no motor?
Our use of the motor was fairly minimal; what if we had used our lovely oars instead? Would an electric propulsion system have served as well? For these questions, we have some data!
To my eye, hanging a motor on the transom of our Core Sound 20, Dawn Patrol, is a bit like painting a mustache on the Mona Lisa. We built the Dawn Patrol for WaterTribe adventure races, for daysailing, and for coastal cruising. We carry beautiful 11’ oars from Shaw & Tenney. I never envisioned needing a motor. So… when Steve Earley suggested the wonderful idea that we bring Dawn Patrol and tag along with the Spartina on a spring cruise, I had to think hard about painting on that mustache. The photogenic Spartina hides her motor in an engine well. Unfortunately, the stern freeboard on our Dawn Patrol is too low for hiding a motor. If we followed the proposed routes, would we be able to keep up with Spartina? “Yes”, if we packed a motor. Without a motor, wind and tide would probably dictate some on-the-fly route changes and delays. Good friend Ken generously offered to lend us his 2 hp, 28 lb, 4 cycle, Honda outboard. We charted and considered possible route variations and alternatives that might work well for sailing and rowing without a motor --as usual. Ultimately, we decided to follow the adage “When in Rome, do as the Romans.” We gratefully borrowed Ken’s motor. It was a good choice. The cruise was a great new learning experience, we were able to have a relaxed enjoyable time, and we had a blast cruising with Steve and Bruce. The many advantages of cruising with a motor made the trip more pleasant, saved us time for favorite activities, and avoided rowing in high temperatures. Given that we have a motor onboard, the disadvantages of carrying the motor (visually unappealing, extra weight, sheet snags on the motor (rarely), having to store the spare fuel somewhere) are not ameliorated by minimizing its usage. If I’m paying the price of these disadvantages, it would be foolish not to benefit from the advantages.
Our GPS Track
We used a Garmin GPSmap 76csx handheld chartplotter set to store our track by recording the latitude and longitude (lat, lon) every 20 seconds. The actual elapsed time between points was variable but averaged 20 seconds. There were a few (lat, lon) values in our track that were obviously in error. Each of these was easy to spot because the corresponding instantaneous speed was rediculous; e.g., 256 knots. The best thing to do is to delete such points from the track --which is exactly what I did. BlueChart software from Garmin was useful for charting our track and allowed me to export the data [lat, lon, time] to the GPX format (i.e., special HTML code) for use with other software.
Speed
In the speed graphs for our cruise, contributors to large variations in our speed included beating upwind into chop, tacking, and varying winds. For example, when beating into chop our speed can alternate rapidly between 6 knots and 2 knots. In contrast, our speed was much more constant when the hull was planing at 7 knots or when we were running downwind at 4-5 knots.
A little motoring
We traveled 207 nautical miles (nm) according to our GPS. Of those, 29 nm relied on the motor or motor+sails. We used a total of 0.95 gallons of gasoline (3.6 liters). Most of our uses of the motor were arguably optional but were desirable for convenience, for saving time and staying on schedule, or as a remedy for crew fatigue and impatience. We relied on the motor the most on Day 4 during 3 hours (9 nm) without wind and via narrow channels. In that case the alternatives included waiting for wind, rowing in the heat of the day, or changing our plans and perhaps rowing after sundown, or combinations thereof that would put us off our intended schedule.
For our next cruise
Would I use an outboard on our next multi-day cruise? Yes, probably. In the past I’ve enjoyed cruising (and racing) without a motor. To do so requires careful planning, a flexible schedule, and a patient crew. Cruising with a motor gives the crew more options and greater control over their schedule so that a desired route can be followed without delay or modification. The choice of whether to leave the motor at home depends on considerations that include the weather forecast, the routes desired, crew preferences, crew characteristics, and any scheduling constraints. How do I feel about about the motor now after our June cruise? To my eye it is still as visually unappealing as a moustache on the Mona Lisa, but I have a greater appreciation for the advantages and options it gives the crew. It may be relative quiet as motors go, but the noise it makes reminds me of a jackhammer. But, if I have to look at that darn thing while sailing, then I’m certainly not going to hesitate to use it for convenience. Like every aspect of small boats, the motor has its advantages and disadvantages.
Choice of motor
I expect we will buy our own Honda 4-cycle, 2-hp, air-cooled, long-shaft outboard in the near future. This is a relatively simple engine seems more than adequate. A less conspicuous and quieter motor would be preferable. An electric motor might be used, but with the current state of battery technology an electric propulsion system could be heavier and less capable than an internal combustion engine. Battery power might be expected to deliver 3 hours of propulsion (as was needed on Day 4), but for a multi-day cruise we would need an adequate number of batteries recharged by large solor panels and a small wind generator --which would still lead to having nappealing machinery mounted on the boat.
Day 1
Total: 13.1 nm in 3.9 hours
Motor: 0.3 nm in 0.3 hours
June 18. The light breeze and flat water at the friendly boat ramp and low dock at Potter’s Marine made launching down North Creek a piece of cake. Sailing away from the dock would have been too easy. Instead, we decided to start our trip by making our very first use of the motor --just to gain some experience with it. I started the motor, reversed it, and backed away from the dock. The slack main sheet immediately snagged on the end of the dock. Darn! Lesson learned, we un-snagged and motored away for three minutes toward the Pamlico River, and then switched to the beautiful quiet of sailing without the aid of internal combustion. The wind was ESE at 11-12 knots as we tacked down the Pamilico River passing Indian Island and Reed Hammock. Our speed dropped from 5-6 knots to 2 knots after entering Goose Creek and the ICW. We spotted Spartina at anchor in Wilkerson Creek (faux Dixon Creek) and headed in tacking at 1 knot. Spartina had started and arrived 1-2 hours ahead of Dawn Patrol. They had tacked right up to the entrance of the creek (to within 500 feet of their anchorage) and then the wind was blocked by trees so they cranked the outboard and maneuvered in. By the time we had tacked to the entrance it was dinner time and we were eager to arrive. In the vanishing headwind some alternative propulsion was desired. Our oars were already mounted in the oarlocks so we rowed for a few minutes before impatiently deciding to motor on in and to “raft up” next to Spartina. After dinner we stowed the oars in their usual place under the cockpit’s coamings --where they remained for the next seven days.
In the SPEED figure below, instantaneous speed values (black dots) are shown with connect-the-dots (tan), smoothed trend (red), and intervals of motoring (gray band). The MAP image below shows the path of the Dawn Patrol (red track) and the path of the Spartina (black dots).
Day 2
Total: 26.1 nm in 10.3 hours
Motor: 2.3 nm in 0.8 hoursJune 19. With SE winds 4-9 knots we sailed south and southeast 5.2 miles down the ICW. Our speed ranged from 1 to 5 knots and eventually depended on frequent short-tacking as the ICW narrowed. By the time we could see the Hobucken Bridge we were ready to power up the motor. We cruised the narrow ICW with the motor for 2.6 miles, at about 2.8 knots, until the waterway widened into Gale Creek. Along the way we passed up the opportunity to follow Spartina out Jones Bay so that we would have an hour to visit Graham Byrnes. After having listened to the motor for 50 minutes we were happy to switch back to quietly short-tacking out toward the Bay River. Our speed varied from 2 - 4 knots while short tacking, but once headed on a broad reach in the Bay River our speed was constant at 4 knots. Raising the mizzen stays’l bumped our speed up to 5 – 6 knots. At Chapel Creek we visited Graham Byrns and his daughter Beth at the dock and workshop of B & B Yacht Designs. Graham took a moment to snap a few photos of the CS20 Dawn Patrol which, apart from the cabin, was entirely his design. It was a real treat to see Graham and Beth, and to see the exciting projects in the B & B workshop. At the moment they were busy finishing (spraying glossy red paint on) the efficient powerboat “Marissa” --his award-winning design. After a swim to cool off from the mid-day heat Dawn and I headed back out on the Bay River toward Bonner Bay where Steve and Bruce were looking to catch some fish. With afternoon temperatures above 90F thunderstorms threatened in the distance and the wind was shifting locally from E to NE. Turning SE into Bonner Bay gave us a good 4-5 knot ride to our anchorage in Long Creek. It has been a great day. Motoring those 2.6 miles at 2.8 knots for 50 minutes in the narrow ICW contributed to that. The alternative would have been rowing at perhaps 1-2 knots into a very light headwind for probably 150 minutes on a hot day. That would be fine if we were doing an adventure race, but less desirable for a vacation cruise.
Day 3
Total: 25.1 nm in 7.39
Motor: 3.7 nm in 1.7 hours
June 20. With a favorable WSW wind at 5 knots, it seemed that we would start the day by sailing downwind through the narrow channel of Dipping Vat Creek toward Pamlico Sound. The narrow channel turned out to be partly obstructed by a pier and an overhanging raised gate. While we were slowing our approach and still trying to come close enough to get a good look at the obstructions, Spartina squeezed through on their second try. Still moving forward at less than 1 knot, we elected to play it safe by dropping our masts. Beaching the bow onto a mud bank brought us to a stop. We lowered the sails, rotated the masts down, and gathered in loose lines in less than two minutes. We could have rowed or skulled through the gate but… we had a motor! We powered through the gate and continued motoring for another 12 minutes the entire length of the 0.4 mile-long ditch at 3.5 knots, the wind at our backs. Yes, we easily could have rowed most of that, or even raised sails again just past the gate. At the end of the ditch we dropped anchor in Fisherman Bay. Five minutes later the masts and sails were up, the anchor was onboard, and we were away. Our speed jumped up to 5-6 knots and stayed there as we rounded Maw Point and entered the mouth of the Neuse River. The route to Oriental gave us 2 hours sailing on a reach and then 3 hours doing a few long tacks back and forth across the Neuse River. Our last tack was too long as it took us to the far side of the river just as there was a lull in the wind. We needed two more tacks to reach Oriental. Where were the winds kicked up by those typical afternoon thunderstorms? There were no thunderstorms. After thirty minutes of creeping along at 2.5 knots and roasting in the 93° (F) heat, we decided to use the motor. After about 25 minutes of motoring toward Oriental at 3 knots, we saw no sign that the wind would return and we opted to furl the sails as we cruised along. After that it took another hour to reach the harbor and the Oriental Inn Marina docks. The wind did pick up again during that hour, but we motored on eager to arrive because the heat was oppressive in spite of our hats, sun glasses, and the many liters of water we were drinking. By 2:15 were were sitting in the oasis of air conditioning in the Oriental Inn’s restaurant. Sipping numerous glasses of ice-cold tea, I felt my temperature drop to normal and my energy return. At about that time the wind out on the river was strengthening to 10-15 knots. We could have patiently waited for the wind, perhaps by taking a swim around the boat, and probably could have arrived in Oriental by 3:30 without using the motor. But as we enjoyed cold drinks in that heavenly air-conditioned oasis, we were thinking “it’s really hot out there” and not “we should still be out there.”
Day 4
Total: 39.5 nm in 11.5 hours
Motor: 9.1 nm in 3.0 hours
June 21. The downwind run wing-on-wing eastward across the Neuse River was wonderful. The wind was increasing and our speed steadily climbed from 3 knots to 5 knots by the time we reached Turnagain Bay. It seemed that we would be able to sail downwind straight through Old Canal and then Thorofare Canal. But no. Somehow there was little or no wind in those narrow canals. In the bays between them we occasionally caught a little breeze. Dozens of dragonflies found us and made themselves at home on the Dawn Patrol and the Spartina as we motored, or occasionally motor-sailed, from the entrance to Old Canal to the exit from Thorofare Canal. We motored for almost 3 hours covering 9.9 miles (~3 knots per hour). Approaching the Thorofare Bay Bridge we passed through a tiny whirlwind (a ‘dust devil’ on land). We noted a few darkening clouds. As we sailed out of Thorofare Bay toward Core Sound, the western sky continued to gradually darken. On the eastern horizon Core Banks remained in full sun. The route down Core Sound was upwind. Tacking and following marked channels was a challenge. Our speed ranged from 3 to 6 knots due to frequent tacking and varying wind. By 2:00 as we passed Drum Inlet the western half of the sky was black and threatening. It was obvious that the storm was moving east, toward us, and it appeared that there was no way to dodge or out-run the thunder storm. At about 2:40 pm as the lightning and thunder approached closer we hove-to for a few minutes to don our foul-weather jackets and to put two reefs in the main and two reefs in the mizzen. Fortunately, we had reefed just in time. As the storm came further out over Core Sound (and us)… it vanished! In a matter of 30 minutes the sky changed from ominous black to clear blue. There were no clouds to be seen. Where did they go! That’s not what we were expecting, but who’s complaining? We hove-to at 3:15 to shake out all the reefs and shed the rain jackets; but his time rather than heaving-to in the usual manner, we cranked the motor and powered directly into the wind at about 3.5 knots for 7 minutes. This motorized alternative to the usual method of heaving to (fully sheeting in the mizzen and releasing the main sheet) stabilized the boat inspite of the confused chop, made the movements of sails more predictable, and did not require sheeting in the mizzen.
With full sails we tacked onward at 4-5 knots occasionally enjoying higher bursts of speed. After working our way far enough down Core Sound, we turned east for a short fast downwind ride over shallower water into The Swash --a tiny bay in Core Banks.
The Swash is a good place to be on a 93° (F) day. The evening was hot but there was a pleasant 10 knot breeze. We anchored in 4 feet of clear cool water and took a dip to cool off. As Dawn and I wondered how we could use the breeze to cool the cabin for more comfortable sleeping, we happened to think of rigging a wind scoop to direct the breeze into the companionway. Surprisingly, my rain jacket and four pieces of string made a perfect wind scoop. We enjoyed a constant 10-knot breeze funneled into the companionway that night. Aaahhhh! It was wonderful. We vowed never to cruise without a wind scoop henceforth.
Day 5
Total: 18.8 nm in 5.2 hours
Motor: 0.0 nm in 0.0 hours
June 22. The morning winds were more-or-less SW at 6-10 knots. We sailed SSW down Core Sound at 2-5 knots to the eastern end of Harkers Island. There we turned SSE and cruised at a consistent 6.5-7.5 knots toward Cape Lookout Light on Core Banks. This fast hull-planing ride was the fastest of our 8-day cruise. (The hull speed of the Core Sound 20 is in the neighborhood of 6.2 knots.) Our speed dropped and became much more variable, at 2.5 – 5.0 knots, as next we tacked SSW through Barden Inlet past the lighthouse. Finally, we turned west on a 3-5 knot reach to Power Squadron Spit. There we planted our anchor right on the beach and immediately began “chilling” in the cool clear water. Arriving at noon gave us an entire afternoon of cool swims, hopeful fishing, and walks on the beaches. It was another hot day but what a great place to be on a hot day. A sunshade tarp rigged above the cockpit and the makeshift wind scoop cooling the cabin made our visit all the better. And, three cheers for a day without using the motor! Well…. almost. At dusk we did use the motor for a minute to relocate the anchor 50 feet out in deeper water. Yes we could have used the oars instead.
Day 6
Total: 13.8 nm in 3.6 hours
Motor: 2.4 nm in 0.6 hours
Using our GPS we closely retraced our track from Day 5 back to the eastern tip of Harkers Island. The wind was SW 8.5-13 knots giving us an easy 5-7 knot ride out of Barden Inlet and into Back Sound. That was easy! (Where is the that-was-easy button when you need it?) We then turned west to cruise along the Harkers Island waterfront more-or-less successfully following the channel markers to Taylor Creek. Going around the Middle Marshes I happened to notice that the GPS said 5 knots but visually it appeared we were moving through the water at only 1-2 knots. We were riding a conveyor-belt of current toward Taylor Creek. The entrance to Taylor Creek featured a red nun buoy lying on its side high and dry on a sand bar, current going our way, and a sudden lack of wind as we passed a stand of trees on Carrot Island. Dawn had previously fretted about sailing/rowing in Taylors Creek (worried about collisions), so we started the motor and began dropping the sails as we entered the Creek. Once in Taylors Creek, we could have sailed but I knew that with the motor puttering along Dawn was happy at the helm, able to relax and enjoy the view of interesting boats and waterfront. We motored to Beaufort Docks marina (37 minutes, 2.7 miles). The dock manager directed us, Dawn Patrol and Spartina, to a pair of slips. We maneuvered there by motor (6 minutes, 0.17 miles).
Day 7
Total: 35.0 nm in 10.4 hours
Motor: 10.2 nm in 2.5 hours
June 24. At 6:00 am the winds in Beaufort were generally SW at 7 knots. We motored away from Beaufort Docks marina at 6:15 hoping to reach the drawbridge around the corner just in time for the 6:30 opening. We did not want to miss it because we knew the bridge would not open again until 8:00. It is likely we could have sailed to the bridge. But… we had a motor! Dawn prefered that we motor through the bridge. Fifteen minutes and 0.5 mile later we motored through the open bridge while thanking the bridge master. We motored another thousand feet into the Newport River before switching to sail power. The morning was beautiful out on the river. Our 4-6 knot downwind open-water speeds began to drop as we entered the ICW and sailed further and further up the narrowing waterway. At 8:25 we had reached the NC 101 bridge and our downwind run had faded to only about 2 knots. We started the motor and cruised at about 5 knots the next 6.3 miles (70 minutes). By 9:35 the waterway had widened to more than 400 yards and we were able to switch back to sails only. Compared to our relatively constant speed while motoring, our speeds from 9:35 to 11:15 in Adams Creek were quite variable due to the varying winds in the creek and due to frequent short tacking. By 11:15 we had escaped into the open waters of the Neuse River. Out on the river the wind was inconsistent. We spent the afternoon hunting the wind. At 2:15 we were passing Great Island and the mouth of Clubfoot Creek –gateway to the Harlowe Canal waterway. By 2:40 we were on the last long leg (bearing 310° true) of the transit to Beard Creek. We sailed close-hauled into very small chop because the wind had shifted to being primarly a west wind. Speed varied from zero to 5 knots. After our speed had dropped below 2 knots several times, we chose to start the motor (3:15). With the sheets released and both sails luffing we adjusted our speed to 2.5 knots. Then, sheeting in to take advantage of any breezes, we found that the sails often added 3.0 knots to our total speed. The motor kept our speed more consistent through the chop and the lulls. We motor-sailed 4.4 miles (65 minutes). The wind gradually strengthened. At 4:20 we rested the motor and sailed the remaining 2.1 miles to our anchorage in Beard Creek. Meeting up with Spartina there, we also used the motor momentarily to maneuver. In total we motored 11.3 miles during 155 minutes. Without a motor our day would probably have been at least 2-3 hours longer. That assumes we would have sailed to the drawbridge in time, rowed the 6.3 miles in the ICW, and patiently sailed the last leg to Beard Creek. Having the motor kept us on schedule --arriving at anchorage in time for a relaxing dinner by 5pm.
Day 8
Total: 11.6 nm in 3.6 hours
Motor: 1.1 nm in 0.5 hours
June 25. How much was our speed reduced by sailing to New Bern with the ladder down? We’re not sure because we have not yet tried to measure that effect. After taking a cooling dip in Beard Creek the previous evening, I had neglected to fold it back up to its upright locked position. The ladder is mounted on the transom so that it is not visible from the cockpit. We sailed out of Beard Creek at 2-3 knots and sailed close hauled on a single bearing all the way to New Bern without realizing the ladder was dragging. The wind over our route was generally SW 4-6 knots with occasional gusts and lulls. In this more-protected part of the Neuse River the water was flat --chop and waves mostly less than 8 inches. Variability in our speed was relatively small. In the absence of sizable chop/waves, currents, and tacking, the only factors that remained to account for the variability in our speed were changes in wind, sail trim, and hull trim.
At 9:15 we were within a mile of the high bridge over the Neuse (US17) when we heard Steve’s conversation with the drawbridge master: “… and there’s another sailboat right behind us…” or something to that effect. We quickly started motor-sailing at 5 knots but almost immediately realized we were too far away to hurry. I regretted starting the motor too soon but decided to go ahead and power in because the wind had faded. We furled the sails and motored under the high bridge, through the drawbridge, and into the New Bern Grand Marina. After docking in our slip we noticed the ladder.
It was a hot day. From a low of 78° at 6:00 the heat climbed to 85° by 9:00, to 90° by noon, and top out at 95° (F) as we explored New Bern on foot.
In the SPEED figure above, instantaneous speed values (black dots) are shown with connect-the-dots (tan), smoothed trend (red), and intervals of motoring (gray band). The MAP image above shows the path of the Dawn Patrol (red track) and the path of the Spartina (black dots).
--Paul
Very interesting reading, Paul. Thanks. Your presentation and analysis makes the data really useful.
ReplyDeleteIt would be interesting if you took another trip and borrowed a good electric trolling motor for comparison. I would love to hear your thoughts on both after that trip.
I'm very, very protective of my peace and quiet. I use an 82lb 24volt trolling motor on my 12 foot skiff. I've never run the two batteries down, so don't know exactly how long they would last, but it has pushed the boat and two people at 4-5mph (about 70% throttle) all day long many times for 5 to 6 hours straight. At the end of one of those days I would estimate there's about another 3 to 4 hours in it at 50% throttle.
On the short boat, hull speed is quite low. Trying to go faster is an exercise in diminishing returns. I could easily run two full days if I stayed at 3mph. Dawn Patrol is longer, so you could go a tad faster for the same power.
To some extent, there's no comparison between gas and electric - they're just too different. One is loud and smelly and finicky, and requires regular maintenance, but you can refuel in minutes and be on your way. With extra fuel on board the range is virtually unlimited . The other is silent, reliable, and maintenance free, but requires an overnight at a marina or in town to "refuel" when you run dry. (I don't consider extra batteries and multiple charging systems practical, yet.) Small non-planing sailboats just happen to be one of the few types of boat where their respective virtues cross over to such an extent that you actually have a choice.
In other words, I think you really do have a third option besides gas motor only, or oars only. You'd always have oars for backup, which would be no worse than no motor at all. You could definitely use it for drawbridges and canals, and motoring into harbor when the wind dies. If your trip included a stop overnight at a dock mid-week you'd probably never have to use the oars. Since you favor quiet and esthetics as well, it would be interesting to hear your thoughts after doing a comparison.
Thanks for the thoughtful comment, EyeInHand. I appreciate that you've highlighted the third option and did so from first-hand (first-eye?) experience. This post did not give that option its due. However, I have thought about saltwater trolling motors and dreamed of having a nice electrical system that includes a small but fast-charging solar panel (not invented yet) and a tiny but efficient and storable wind generator (also not invented yet). I just barely tolerate the thought of carrying a 28 lb motor, so heavier propulsion systems have seemed less desirable. For expedition racing we will only carry the oars. For cruising, there is the question 'how much weight am I willing to pack if it means we have quiet propulsion?' Good to think about and investigate further.
ReplyDeleteThe weight is an issue, of course. It works best when the batteries stay on the boat, replacing otherwise required ballast. Then there's no weight penalty, and you don't ever have to move them. (I don't think the Core 20 needs ballast, though?)
ReplyDeleteI think of it as bringing along an extra crew member who does nothing but row when we want some rowing. Doesn't eat much, and doesn't talk much, but works hard. Perfect companion.
I've seen people cannibalize high voltage cordless power tool batteries, making plug-in housings to get various power arrays. They're expensive, but they pack a lot of power in a small lightweight package, so they can carry extra batteries. They also have the added advantage of charging in minutes.
You wouldn't guess it, but some of the more advanced commercial electric cars do the same thing, buying the same little batteries in bulk from the manufacturers. You open the big battery pack and it's nothing but a hundred small cordless drill batteries wired in series and parallel. The technology is getting better slowly.
Ah yes, the 82lb perfect companion. Very quiet. Ready to "row".
ReplyDeleteYep, the CS20 was designed to not have any ballast other than the gear and sailors onboard.
Nevertheless, some CS20 and CS17 sailors have added 10-20 lbs of weight to their centerboards and/or rudders, and some carry a heavy battery onboard (positioned to be useful as ballast, of course.)
--Paul