The 1779 Tax Assessment for Hanover Precinct, Ulster County, New York - Part II

In December 1779, two hundred and forty-five years ago, David Galatian, the Hanover Precinct supervisor, rode his horse down a dark, frozen dirt road in Ulster County, New York to the Rock Tavern.  He was retracing his steps past homes he had added to his assessment list earlier that day.  At the tavern he hoped to find drink and conversation.  Perhaps one of the men in the crowded room was Joel Campbell, eponym of this blog. (Also see Part I.)

The young country had been at war for over three years.  Washington’s continental army was wintering near Morristown, New Jersey. The soldiers were low on food and winter clothing.  Washington had pleaded to the Continental Congress for supplies, but even if purchases were granted, the Continental currency had lost much of its value and could buy little.  His troops foraged local farms. 

The weather was also turning cold.  The muddy ruts formed by rains and wagons earlier in the month had been turned to frozen corduroy by a persistent cold air mass.  As was common, about half of the continental army had returned to their homes for the winter.  Undoubtedly some of the men of Hanover were such soldiers, perhaps even a few drinking on this night at the Rock Tavern.

The states also maintained militias. In New York, the governor was commander in chief of the militia.  During this period of conflict, the governor’s military role dominated his attention.  The New York Assembly passed an Act in October allowing for the collection of a tax to support the military.  It authorized Galatian to create a list “for raising their [Hanover Precinct’s] quota of [the] two million five hundred thousand dollars by tax by an Act passed for that purpose October 25, 1779.”  He went on to write on the first page of the completed list, “The quota of Hanover is 16494 pounds which is raised in this list with a surplus of 170.”

1779 Tax Assessment Summary

Joel and his brothers were living is this approximate area in 1779, so they should be listed in the assessment.  (His sister, Mary Norris, was still in New Jersey and their father had died about 5 years prior.). His brothers with their guessed ages were Samuel (47), Daniel (46), Joel (44), Nathaniel (42), Jonathan (40), Reuben (36), Nathan (35), and Levi (26). 

Samuel had received from his father “the land I now live on” in the 1773 Will.  In the tax assessment of 1779 it is listed as 86 acres with a value of 144 pounds.  His personal wealth is listed as 56 pounds.  This is probably farm equipment and livestock.  His brother, Nathaniel, appears to be living on his land.

Samuel and Nathaniel in 1779 Tax Assessment

Also living in close proximity are several Munnels (also in the records as Monnel or Munnil), Hills, and Teunis Van Asdall.  They were known to live close to the intersection of what is now 208 and 17K, which gives us an idea of where Samuel’s farm was.

The Rev Andrew King, who appears three lines above Nathaniel and Samuel, was the pastor at the Goodwill Church that is still located on 208 just south of the intersection with 17K. He would perform the marriage of Joel's daughter, Jemima, and Joseph Tice in about 6 years. (There are 3 Tice/Tise entries in the assessment.)

The relationship of  Phinely Campbell, who appears on this page, is unknown.

Daniel had received the original Campbell farm in the will of 1773. But in the 1779 Tax Assessment he had no real property (the farm appears to have been sold to his brothers, Nathan and Levi. See below.) and his personal property was only 12 pounds. He is living close to the Crist's mill and perhaps is employed there.

Daniel in 1779 Tax Assessment

Nathan and Levi are farming next to John Perry, Benjamin Wood, and Benjamin Haines.  This fits the description of the original farm willed to Daniel.  The sum of 50 acres matches the amount described in the will.  These are very small farms for large families.  Their personal wealth is also very small compared to their neighbors.

Nathan and Levi in 1779 Tax Assessment

A farmhouse of a Benjamin Haines (there were several generations with this name) still exists on Coleman Road in what is now called Montgomery Township, Orange County, New York.

Gideon Pelton, who appears near the top of the list, eventually owned a large farm 2 or 3 miles to the south.  That farm and farmhouse still exist and are historic landmarks.

Jonathan is living in Shawangonk(sp) Precinct just to the north of Hanover Precinct.  He is the most prosperous of his siblings by far.  The value of his real property is 1000 pounds (500 to 1000 acres?) and has personal property of 1000 pounds.  It is likely that his wife, Mary Heines (Haines), inherited the farm of her father.

Jonathan in Shawangunk Precinct Tax Assessment

Missing are Reuben and Joel. Reuben may have already moved west into Mamakating Precinct where he was living in 1790.  That assessment has apparently not survived.

Joel's absence is more of a mystery.  We know he lived in this area in 1767 (Colden Store) and in 1790 (US Census for Montgomery (aka Hanover)).  A "Joel Campbell" is named in an April 23, 1779 list of “exempts” in the Company of Captain Jacob Conklin, in Jonathan Hasbrouck’s 4^th Ulster Regiment of Militia. [History of Orange County, Ruttenber, Edward M. Philadelphia, 1881, p 49.]  Conklin's was known as the "Western Newburgh Company" and was said to be "recruited in Wallkill." [see Article in New York Genealogical and Biographical Society Journal, Vol 59 Issue 4 p223.]  Hasbrouck's regiment was recruited out of the precincts of Newburgh, Marlborough, and Shawangunk.  Most of the surnames on the list can be traced to families in Newburgh or New Marlborough. The tax assessments for Newburgh and Marlborough have not survived.

The 1779 Tax Assessment for Hanover Precinct, Ulster County, New York - Part I

[Also see Part II of this Article.]

The 1779 tax assessment for Hanover Precinct, Ulster County, New York is the most complete list of residents I have found of the inhabitants of this area during the Revolutionary War.  It is the bridge between the US census of 1790 and the list of shoppers at the Colden Store of 1768.  

If you are new to researching this area, it was renamed to "Montgomery Precinct" in 1782, "Town of Montgomery" in 1788, and became part of an expanded Orange County in 1798. 

I believe I first saw the tax list on microfilm at the New-York Historical Society, but I later was given a pdf copy by a local historian who I sadly cannot remember. I referenced it so often that I transcribed it to a spreadsheet which I could sort and search. Finally, today I loaded the searchable 1779 Tax Assessment database to the OCHS website, so others can find and use. 

I wrote about this tax assessment in my biography of Joel Campbell, Yeoman of the Revolution.  I incorrectly suggested that John Blake prepared the census, but I have later discovered it was prepared by David Galatian. I wrote about the Galatian family.  David would create the 1798 map of Montgomery and would be its first supervisor upon creation in 1798.

Because I had a known relationship to all of the Campbells in this tax assessment (except for Phinely who was a tenant of Colden), I thought there was a good chance that a Campbell who joined the Hanover militia in 1776 was probably also related. This is the Andrew Campbell written about in prior blogs.  YDNA has shown that is not the case. More on that soon.

Reuben Campbell - from Newark, NJ to Ulster, NY to Ovid, NY

The rapid western expansion in the 1820s and 1830s often complicates genealogical research. A name disappears in New York, and now appears in Indiana, Ohio, Illinois, or Missouri.  Is it the same person?

One example of this is the families of Reuben and Simeon Campbell who are enumerated in the 1810 census for Ovid, Seneca, New York. 

How Reuben and Simeon are related is still unknown, but it is assumed they were cousins.  Both were born in New Jersey.  Reuben relocated with his father to the Wallkill area of New York (current Montgomery, Orange County) in about 1765.  He first appears in the records of the local store in 1768 purchasing sugar and molasses and picking up items for his brother, Jonathan, to whom he may have been apprenticed as a blacksmith. He is confirmed to be the son of Samuel Campbell in a will of 1773.

His name first appears with Simeon's in 1775 when they both sign the Articles of Association in New Paltz. We know Simeon to be born in 1754 from his enlistment in 1776. Reuben is guessed to be a bit older, perhaps born in 1745. Reuben moved again with many of his brothers to the western part of Ulster County.  His farm in Mamakating neighbored that of Simeon in the 1799 tax assessment roll. In 1802, Reuben and his son Thomas appear on the tax assessment roll for Ovid, Cayuga County. Simeon soon appears in Ovid in the 1810 census. 

Pages 19 and 20 of the 1810 census for Ovid contain many surnames that are interwoven with Reuben and Simeon Campbell: King, Leonard, Russell, Ludlow, Conklin, Garrett. 

The changes to this area of Ovid are apparent in the 1820 census. Reuben and Thomas are missing. Simeon's close neighbor, Benedict Russell has left a 26-44yo widow, Abigail. [Could this be his daughter?]. Simeon has gained a new neighbor, widow Lydia King (26-44) with small children. [Could this be another daughter?] His close neighbor, Silas Ludlow, has been replaced by his son, Samuel Ludlow, husband of Hannah Campbell (Simeon's daughter). There is no older member of the household, suggesting the death of Silas. Further down the page appears Jeremiah King, husband of another daughter of Simeon, Sarah.

It is not until the 1850 census that we pick up on the trail of Thomas, son of Reuben. We discover that between 1810 and 1820 he moved to Ohio with his wife, Hanna, and children, Phoebe, Reuben, and Elizabeth. They are enumerated in the 1820 census of Darke County, Ohio. In 1824, Ohio marriage records show Betsy (Elizabeth) married Marvin Chapman in Darke County.

Albert Nevius relocated at about the same time if not as a group with Thomas.  Albert's daughter, Eleanor, and Thomas' son, Reuben, marry in 1827 in Ohio.

The 1830 census for Montgomery, Indiana shows a Thomas Campbell with a household of six.  The ages for Thomas and Hanna agree with birthdates in later records.  They are living next to Reuben Campbell [presumably their son].

The 1840 census for Fountain, Indiana (a county bordering the west of Montgomery County and just east of Danville, IL) shows a Thomas household of two people.  The ages are correct for Thomas, now 63, and Hanna. Their neighbor is Cornelius Reeson (Ryerson) who is married to daughter, Phoebe. Another neighbor is Boyington Chatman (Chapman, Marvin's brother) Their daughter, Betsy Chapman, is living in the neighboring county of Montgomery, Indiana.

It is not until the 1850 census, when names of each individual in the household are enumerated along with exact ages and birthplaces, that we can put this all together. The 1850 census for Crawford, Missouri shows a 73 year-old T Campbell born in NY; living w 70 year-old H Campbell(F) born in NJ with 19 year-old R Rison [Believed to be Orilla Ryerson, their 19yo granddaughter(F) b in IN.]  They are living next to M(arvin) Chapman 53 born in PA [presumably their son-in-law]. Marvin is living with B(etsy) Chapman(F) 42 b NY [presumed to be Elizabeth their daughter] The birthplaces of the Chapman children suggest they were living in Ohio in 1828, IN from 1831 to 1840, IL in 1841, and MO from 1844.

What became of Reuben? In 1810 he is guessed to have been about 65yo living in the household of Thomas. He does not appear in the household of Thomas in 1820.  I suppose he could be in the household of an unknown daughter. One possibility is that he is the second male older than 45 living in the Simeon Campbell household in 1820?

This proof of a father-son relationship between Reuben and Thomas is not totally bulletproof.  Even the proof that this Reuben in Ovid is the same Reuben mentioned in Samuel Campbell's will of 1773 could be questioned. The knock-out punch was delivered by the YDNA of a living descendant of Reuben, son of Thomas. That YDNA matched that of descendants of other sons of Samuel who were also mentioned in the will of 1773.

Optimizing Bicycle Tire Pressure on Gravel - Part III (The Part where freshly-waxed chain break-in time is revealed.)

This is Part III describing studies to determine which tire pressure gives the least rolling resistance on gravel.  You should read Parts I & II first. Be aware that the results are unique to my weight, tire, and road surface conditions.

[For my genealogy research readers:   You are at the correct location.  As you know I get distracted at times.  More genealogy research results will come soon.  My most recent post on Y-DNA is here.]

In Part I, I found the surprising result (to me) that my drag at a tire pressure of 30 psi was less than my drag at 40 or 50 psi. I calculated the power savings to be about 10 watts. That is similar to the savings I obtained by getting into an aero position (all at about 15 mph).

In Part II, I made some improvements in the testing protocol, but I began to question the reproducibility of the data.

This study, Part III focused on reproducibilty of the protocol. The changes from Part II are:

1) Silca Pump used with advertised accuracy of 1%.
2) Wheel circumference was remeasured using new pump and a 10 revolution loaded-roll-out on smooth pavement. (Average of 5 roll-outs.  All pressures tested had measured circumferences with std dev of less than 0.03%.)
3) New test loop was in a traffic-free, wind-protected dip, with no paved sections.
4) 8 laps per test (vs 4 in Part II). Total distance per test was 2.21 miles vs. 2.09.
5) Freshly-waxed chain

The Test Variables

Only the tire pressure was varied.  All other variables were held constant.  Three pressures were tested: 20, 30, and 40.  The 30 psi test was repeated 4 times to test for reproducibility.

The results are shown in terms of Virtual Elevation (VE). (See Part I for short explanation of VE). The steeper the slope of a Test, the more power is being lost versus other Tests. [Note how much cleaner these data are than in Part I and II.  All of the laps are clearly visible. The VE of the dip is more consistent than Part II (due to lack of paved section?)]

Analysis of the data revealed that the break-in of the freshly-waxed chain overshadowed all of the other variables! The negative impact of using a freshly-waxed chain was about 14 watts during Test 1 versus Test 6. Even after 9 miles of riding there appears to be break-in losses. The abrupt change in slope in Test 3, when the pressure was lowered to 20 psi, suggests there could be some reductions in rolling resistance, making the break-in losses appear less severe.  When the pressure was increased to 40 psi in Test 4, the abrupt change in slope in the opposite direction indicates more loses versus the 20 psi Test.  The flattening of the slope at the end of Test 4 is a bit puzzling. The slope at the start of Test 5 could be viewed as a continuation of the curve begun back in Tests 1 and 2. The last 3.5 miles of riding appear consistent, indicating the break-in is complete.

Conclusion

The objective of showing reproducibility was not achieved in Part III. (Sorry...Part IV is coming.)

The freshly-waxed chain (SRAM 12 sp with SILCA Super Secret Hot Wax) was shown to take at least 10 miles or about 45 minutes of riding to reach a steady state. 

Also see 7:26 minutes into the Silca video: Chain Waxing? Avoid These 7 Common Failures! (youtube.com)

GCN beat me to it.  This Chain Waxing Mistake Makes You SLOW (youtube.com)

Optimizing Bicycle Tire Pressure on Gravel - Part II

This is Part II describing studies to determine which tire pressure gives the least rolling resistance on gravel.  You should read Part I first. Be aware that the results are unique to my weight, tire, and road surface conditions.

[For my genealogy research readers:   You are at the correct location.  As you know I get distracted at times.  More genealogy research results will come soon.  My most recent post on Y-DNA is here.]

In Part I, I found the surprising result (to me) that my drag at a tire pressure of 30 psi was less than my drag at 40 or 50 psi. I calculated the power savings to be about 10 watts. That is similar to the savings I obtained by getting into an aero position (all at about 15 mph).

There were some flaws with that study, which I tried to correct in Part II. The following changes were made to the study for Part II:

1) I used a two-sided power meter instead of one-sided.
2) I measured wheel circumferences at all tested pressures. (Lower pressures have smaller circumferences.  The circumference is a speed sensor setting.)
3) The new loop is at a dip in the road.  This allows for speed variations and easier identification of laps.
4) I started and ended tests at V=0 vs. in-motion starts and stops in Part I.
5) Test on a less windy day.

This study still had some flaws which I think I can address in Part III or IV. They are:

1) My pressure gauge is neither accurate nor precise.  (A new one is on order.)
2) There is a section of paved road at the bottom of the dip. This results in some noise in the data seen at the bottom of each data curve.
3) I only made 4 laps per test (vs. 6 in Part I), but the laps were twice as long as in Part I.

The Test Variables

Only the tire pressure was varied.  All other variables were held constant.  Three pressures were tested: 27, 32, and 37.  The 32 psi test was repeated at the beginning and end to test for reproducibility.

The data are reported as 'Virtual Elevation' (VE) versus distance. An increase in slope indicates more power was needed for that test condition versus the base case. Test 4 is the base case.

The data are a bit cleaner than the data from Part I, however the test is not reproducible from Test 1 to Test 4.  In my next study, I will do a duplicate at the beginning of the study (Test 1 and Test 2) and again at the end, to nail down the variability of this test.

If I use Test 4 as my baseline and choose CdA and Crr that will make Test 4 level, it can be compared to Test 2 and 3. In this case 37 psi is a 3 watt penalty and 27 psi is a 3 watt savings versus 32 psi.

I lack 100% confidence in these results.  However, I have changed my default riding pressure to 28 psi in front and 30 psi in rear, so I do have some confidence that what I am seeing is real.

Part III will be coming soon! 

Optimizing Gravel Tire Pressure using Chung Method - Part I

I am preparing for an upcoming gravel triathlon. What is the optimal tire pressure for me and my set-up on gravel? What if I find myself alone on the bike course with no one to draft behind? ...What is my optimal body position?

Generic "answers" to these questions can be found on the internet, but can I find the optimal conditions for me and my set-up?

I performed the seven tests below in under an hour.  Three of the tests were duplicates to verify that the tests were reproducible (1, 4, and 7).  The test conditions and results are shown below.  They are shown in terms of a "Virtual Elevation" (VE).  If the slope is upwards for a test, it means that extra power is needed for that test (like going uphill).  Conversely, if the slope is downwards for a test, it means less power is needed for those conditions.

In summary, it appears that a tire pressure as low as 30 psi is more efficient for me than 40 or 50 psi. As one would expect, getting into the drops is more aero (negative slope in VE) than being on the hoods.  Even greater savings is seen when I bring my hands in close on the bars (Test #6).

What amazed me was how quickly I was able to do these tests (under an hour) AND despite less than ideal conditions (it was windy, course was flat, and I did not alter speed very much) I had results that yielded valuable information.

Test Protocol

Each test was 6 laps on a quarter mile gravel loop.  The loop was flat.  (Better results are obtained on loops with a change in elevation.) I averaged about 14 mph for all laps. (Better results are obtained if the speeds are varied.) I used a calibrated Garmin Speed Sensor (more accurate than GPS).  I used a single-sided Quarq spindle power meter. (Better if two-sided.)  Tire pressure was measured using a Specialized floor pump with gradations every 5 psi....not that precise and probably not that accurate either. I captured T, RH, and P at the start and end of the test protocol using www.localconditions.com.  I weighed myself and loaded bike using a Tanita floor scale.  Each test was saved as a Garmin workout.  All seven workouts were exported from Garmin Connect as TCX files and imported into Golden Cheetah.  The seven workouts were combined and analyzed in the AeroLab Chart as shown above.

The Chung Method

Virtual Elevation is the output of the Chung Method.  The method solves the Power Balance equation for slope, using guesses for Crr and CdA. Slope multiplied by velocity gives the change in elevation which are strung together and plotted.  This elevation is referred to as "Virtual Elevation" as all of the unaccounted for "power" in the Power Balance, whether it is related to elevation gain or not, is converted to elevation. Chung has shown that this method is good at exposing even minor changes in Crr or CdA, even when the data is crappy...as mine are. You can read his paper here.  [Crr is the Coefficient of rolling resistance and CdA is the Coefficient of drag area.]

Data Analysis

Stringing all of the test data together allows a visual analysis.  I guessed a Crr and CdA which made the duplicate runs (1,4,7) as flat as possible. If the test is reproducible, 1,4, and 7 should all be the same. In fact, each of the 6 laps within a test should be the same.  If you look closely, you can count the 6 laps in each test. Test 1 had some anomalies on the first two laps. I did not do any practice laps. This was the absolute first time I had ever biked this loop. There was a conduit over the road which I rode over on the first 2 laps.  All subsequent laps, I biked around it.  It is interesting that this method is sensitive enough to show that. Test 4 had relatively good data. Test 7 appears OK for the first 3 laps, then trends up. The wind was gusting more, so that could be part of the cause. Considering how windy it was, I am surprised I got any meaningful data at all from these tests. With these differences in 1,4,7, I would want to do this test again on a calm day to confirm the results. 

A note on Test 3: On the fifth lap, a camper pulled out and I had to go onto the shoulder to go around him. On the sixth lap, he was still there. All of that is visible in the virtual elevation plot. Now I know to redo the test if that happens again.

Crr on Gravel

My testing qualitatively showed that my set-up at 30 psi had less rolling resistance than 40 psi or 50 psi.  My tires are tubeless Panaracer GravelKing SS TLC 40 (40-622) (700x38c) tires. I use Silca Sealant. My total weight (biker + bike) is 71.7 kg.

BicycleRollingResistance.com has tested these tires.  They show that the rolling resistance decreases as psi increases....the opposite of what I found in real life!! Of course, their testing is done on a drum that mimics a paved road at 18 mph and 94 lbs load and 70-73 °F. Their Crr are 0.00498 at 54 psi, 0.00528 @ 45 psi, 0.00576 @ 36 psi, and 0.00674 @ 27 psi. You would expect the Crrs to be much higher on a rough surface like gravel.

The Silca Tire Pressure Calculator suggests (for my weight and tire) about 43 psi for Category 1 gravel (well-packed), 40 psi for Category 2 Gravel (not packed), 35 psi for Category 3 gravel (very rough) and about 31 psi for Category 4 gravel (off-road). This is getting closer to the pressures suggested by my testing on what I would call Category 2 Gravel.

My data are not really good enough to quantify a value for Crr for my conditions, but we know it is greater than 0.005.

CdA on a Gravel Bike

The range of CdAs for cyclists vary from 0.2 m² (time-trialers) to over 0.7 m² (riding upright). 

The Chung Method may not always be able to quantify the value of CdA, but one can visually see a change in CdA from one set-up to another.  In Tests 4,5,6, all conditions remained the same except for body position as seen below.

I have also used AeroTune to measure CdA on a timetrial bike and find the Chung method not only easier to perform, but much easier to get a visual feel for the accuracy of the results.

Test 4 - On Hoods

Test 5 - In the drops

Test 6 - Tuck with hands on bar

Part II addresses some of the flaws in this study.

Andrew Campbell b1747 - YDNA

I have a special fascination with an "Andrew Campbell" who served in the Continental Army for all 8 years of the Revolutionary War.

I wrote an article about him for the Journal of the Clan Campbell Society of North America. 

I blogged about his military discharge at Snake Hill in New Windsor, New York.  

I even started an autosomal DNA project to find my improbable 7th cousins. 

I searched for Andrew's descendants and (more importantly) I searched for people doing the same.

It has been over 10 years since the CCSNA article. It has been a long slow journey, a journey that continues. This week marked a huge step in finding out ... Who is "Andrew Campbell?"

As recently as 2020, I believed that Andrew had no paternal descendants. However, another family researcher, Debi L., continued to uncover Andrew's children and their descendants. A few years ago, she found a living paternal descendant.  It took me another few years to make the contact and make arrangements for a YDNA test with Family Tree DNA.  The test is now "in the mail."  Results are expected in a few months.

Why is this so interesting to me and to other descendants of Joel and Andrew? Currently the parentage of Andrew is unknown. His geographical proximity to Joel in 1775 makes a relationship more than a remote possibility.  Joel was in the same local militia company in Hanover Precinct, Ulster County, NY. 

Andrew was in the minuteman company of Captain Peter Hill of Hanover. Joel is enumerated on the same page as Captain Peter Hill in the 1790 census. [The Campbells and the Hills had lived in the area since the 1760s.]  Peter was the son of Nathaniel Hill referred to in a prior blog.  His home still stands.

Andrew also served in the Continental company of Captain William Jackson of Hanover Precinct (as he testified for his pension application in 1818.) Nathan, Samuel, and Robert Campbell were also in a militia company commanded by Jackson the same year, prior to Jackson raising a company in the Continentals. Nathan and Samuel were brothers of Joel. 

Was Andrew a nephew? (son of an older sibling of Joel?) Or perhaps a 2nd cousin (a grandson of a brother of Joel's father.) Or possibly related to the Alexander Campbell family living in that area in the 1760s who were part of the Lachlan Campbell immigration party of 1739...and unrelated. YDNA will answer most of those questions.

Here is the genealogy from the father of the Tester to Andrew:

Arthur L Campbell 1911-1989
Richard James Campbell 1886-1946
Albert S Campbell 1842-1918
Richard Campbell 1798-1869
Andrew Campbell 1747-1833

Ship Wakes and the Kelvin Wedge

This is a continuation of a few "off-topic" discussions, with no more convenient home. My apologies if you are looking for "joelcampbell1735-research."  I will be back to that soon.

Waves

I have spent more time in recent years staring at waves.  I live on a 'coast' and almost daily walk the beach and watch the end of the wave lifecycle as they peak, topple, and crash into the shore.  Occasionally I sail on a tall ship and view the wash basin that is the normal sea.  Waves of all heights, directions, and wavelengths.  Sometimes waves appear organized...traveling in a group, all with the same direction and speed.

Wakes

One well known wave (or set of waves) is that which extends out from the bow of a ship and appears to travel at the speed of the ship.  A similar wake is seen behind a duck, a kayak, or a swimmer.  In fact, way back in August of 1887, William Thomson, announced that these wakes all had the same angle regardless of the speed or size of the moving object.  Thomson, also known as Lord Kelvin, a 63-year-old world-renowned scientist in Glasgow, delivered a lecture at the Conversazione in the Science and Art Museum in Edinburgh, giving the angle as one made by a line from the bow of a ship (x=0, y=0) to a point of x/y = 8^1/2. [If you remember your trigonometry, y/x would be the tangent of this angle, so the angle is....

 tan^-1(8^-1/2) = 19.47 degrees.]

Duck with Wake Waves
Daderot, Public domain, via Wikimedia Commons

Getting to the Solution

How Lord Kelvin arrived at this elegant solution is not revealed in his 1887 address. [You can read the paper at Archive.org]   It has been solved on-line and in textbooks, sometimes with a bit too much fancy mathematics and hand-waving for this author. In my opinion, there is a hierarchy of learning needed to arrive at an understanding of the solution. To understand the wake angle, you need to understand "group velocity." But to understand group velocity, you must understand "gravity waves." But to understand gravity waves you need to understand the "Law of Squares."

The Law of Squares

In nature, many relationships are linear. For example, if you double the speed of an object, then you double the distance the object travels. Other relationships are related by the Law of Squares.  Gravity is one of those. As the distance between two objects increases the amount of mass needed to obtain the same gravitational force increases by its square.  It can be written

g   α   d² / m        

where g is some gravitational constant which is proportional to the square of the distance separating two bodies.

Gravity Waves

Surface waves on a body of water are governed by gravity and are termed 'gravity waves.'  It should come as no surprise that the Law of Squares is involved in the description of gravity waves.  In fact, the speed of a gravity wave is given as 

v = (gL/2π)^1/2  

where g the gravitational constant and L is the distance between wave crests.

You can see that water waves are much different than waves of light or sound.  The speed of light or sound through a media is fixed, whereas water waves travel at many speeds with their wavelengths increasing by the square root of 2 when the velocity doubles.

We can also write the above equation in terms of a wave number (k=2π/L) or

v = (g/k)^1/2

For all waves, frequency (F) is velocity multiplied by the wave number or

F = v k =  (g/k)^1/2k = (gk)^1/2    Sometimes called the frequency dispersion relationship for gravity waves.

Once again, the Law of Squares determines the relationship between the frequency of a gravity wave and its wave number. 

Group velocity

Group velocity is not an easy concept to digest. Fortunately, it can be readily observed. Just this weekend, I sat on my paddleboard and watched a 'group' of waves from a motorboat pass under me. When I focused on the lead wave in the group, I saw it disappear and a new wave appear at the rear of the group. The group had a slower velocity than an individual wave.  The excellent graphic below was borrowed from the Wiki page on Group Velocity, 

On my paddleboard, I was focusing on the red square. But the group is actually moving at the speed of the green dot. 

What causes this? It is the result of the interference of waves of similar wavelengths.

The group velocity (v_g) can be derived as the derivative of the frequency with respect to the wave number or

v_g =  dF / dk

From our equation above for gravity waves for F, the derivative is

v_g = dF / dk = ½ (g/k)^1/2   = ½ v

For gravity waves, the group velocity (the speed of the visible wave front) is one half the wave speed. It is a direct result of gravity waves having a Law of Squares relationship.

Wake  Angle

The wake waves that trail the bow of a ship appear stationary with respect to the ship. They differ from waves generated from a point source, such as a pebble dropped into a pool, from which ripples proceed out in concentric circles.

A moving ship, on the other hand, is continually creating waves, some of which the ship is keeping up with, or from the perspective of a person on the ship, is 'dragging along.' Observationally, there is no doubt that a ship produces waves that appear stationary with respect to the ship and are contained within a wedge bounded by a straight line.

From our earlier discussion, that a wave group moves at one half the speed of the wave phase velocity, one might think that there may be an analogy here to the wedge produced by a supersonic object traveling at twice the speed of sound. In the Figure below, the supersonic object has moved from x=8 to x=0, while the sound created at x=8 has only moved to x=4 (the BLUE circle). Similarly, the sound made when the object was at x=4 has only moved to x=2 (the RED circle). The wedge of sound waves, moving at one half the speed of the object, is bounded by a straight line defined by sin a = SpeedOfSound/SpeedOfObject = ½, or a = 30°.

Even though we have shown the group velocity is one half the phase velocity, the sonic shock wave is not analogous. The ship is generating waves of many speeds and directions that are constantly constructively and destructively interacting with each other. More importantly, the group wave that is stationary with respect to the ship, is the one whose phase velocity matches that of the visible wake, not the group wave that is moving at one half the speed of the ship in direction 90° - a.

Let's look at the problem from a pure trigonometric perspective. We know from observation that there are some wake waves that are stationary and are bounded in a wedge defined by a straight line. We know from our knowledge of gravity waves, that what we are observing are the group waves produced by waves whose phase velocity is twice that of the group. In the Figure below, a ship has proceeded from O to A. The BLACK lines are wave fronts of the waves creating the visible group waves. The group wave associated with this front has only moved to where the RED line appears. The PURPLE line is perpendicular to the phase and group wavefronts, and represents the wave velocity. 

Because waves at this particular (unknown) phase appear stationary, they must have a velocity of v_p = V sin a, where V is the speed of the ship and a is the angle of the phase wavefront with the ship. Hence the visible group wave has a group velocity of

v_g = ½ v_p = ½ V sin a

This is the stationary wave condition that differs from the shock wave situation with sound waves.

As suggested by the trigonometry, the group wavefront orientation and the visible wakefront are not parallel. This is clearly seen in the duck image above. The wake angle, b, is actually created by echelons of short group wave segments.

From this simple sketch of fronts and angles, what can we say about 'a' (the wave group angle) and 'b' (the visible wake angle)?

We can use the rule of trigonometry that the sine of any angle of a triangle divided by its opposite side is a constant. Take the triangle formed by OPA. Its angles are b, π/2 - a, and π - b -(π/2 - a) = π/2 - (b - a).

We can then write

sin(b)/OP = sin(π/2 - (b - a))/AO   Eq.1

where AO = Vt where V is the ship velocity and t is the time to move from O to A
and OP = v_gt = ½ v_pt = ½ Vt sin(a).

We can rewrite Eq.1 as

sin(b)/[½ Vt sin(a)] = sin(π/2 - (b - a))/Vt

Knowing that sin(π/2 - X) = cos (X)

we can write    2sin(b)/sin(a) = cos(b - a)

Interestingly, the relationship between these two angles is independent of the ship velocity, V, which is what we observe.

We can perform more trigonometry to solve this equation, which I will show. If this is of no interest, skip down to the result shown in Eq. 2.

Multiply both sides by sin(a)

2sin(b) = sin(a)cos(b - a)

But 2sinAcosB = sin(A+B) + sin(A-B)

So 2sin(b) = ½[sin(a+(b-a)) + sin(a-(b-a))]

4sin(b) = sin(b) + sin(2a-b)

3sin(b) = sin(2a-b)  Eq.2

The right side of Eq. 2 must be ≤ to 1. Therefore

sin(b) ≤ 1/3

b ≤ sin^-1(1/3)

b ≤ 19.47 °

So the visible wake angle must be 19.47 ° or less. This agrees with more robust derivations of the wake angle.

We can also solve for the angle of the group wave front, a. Once again, the right side of Eq. 2 must be ≤ to 1.

sin(2a - b) ≤ 1

then 2a-b ≤ π/2 or 90°

2a ≤ 90° + b

a ≤ (90° + b)/2

a ≤ 54.7°

Simple trigonometry has led to values for the Kelvin wake angle and the angle of the visible group waves. [Note that the Figure above is constructed to scale with a = 54.7° and b = 19.47°]

Wavelengths

One last simple observation can be made about the wake waves seen in the duck picture above. We know that the wavelength for gravity waves is given by v = (gL/2π)^1/2 or L = 2πv²/g. If the speed of the ship is driving the waves of most interest, then L = 2πV²/g. Because the still picture cannot tell us how fast the duck is moving, perhaps we can guess by measuring the distance between the echelons in the duck wake. It looks like there are about 2 wavelengths per length of the duck. If the duck is about 12 inches long, the wavelength is 6 inches, L/2π =  about 2.4 cm.

V = [9.8 m/s² x .024 m]^1/2

V = [3.1 x 0.16] m/s

V = 0.5 m/s or about 1 mph

My swim speed is about 2 mph, so the result seems reasonable.

The reader can find many derivations on the internet with much more scientific approaches to derive the wake waves and their patterns. But we have been able to confirm some of our observations of wakes with just a knowledge of gravity waves, group velocity, and trigonometry.

Cycling Power Strategies on Out-and-Back Course with Headwind/Tailwind

Suppose you are cycling on a flat out-and-back course on a windy day.  The first half of your ride is into the wind, the second half is with the wind. Is there any advantage to expending more power during the headwind half vs. the tailwind half?

This should be simple to calculate? To compare scenarios, we will specify that the time-average-power (P_average) be a specific value.  In equation form this is...

TotalTime x P_average = P₁t₁ + P₂t₂

The time spent at P₁ (into the wind), t₁, will be longer than the time spent at P₂ (with the wind).

The other assumption we will make is that our 'air speed', W, is high enough that most of our power is consumed in combating drag. We can write...

W₁ = kP₁^1/3       

...meaning the air speed is solely a function of a drag coefficient, k, times power to the 1/3rd power.  This is a fairly good assumption at air speeds over 20 mph. This relationship tells us that to bike 10% faster, we need to increase power by the cube of 1.1, or about 33%.  [It also suggests that efforts to reduce k (a 'drag coefficient') can pay dividends when power increases are hard to find.]

The 'ground velocity', V, (what appears on your cyclocomputer) is W-w, where w is the wind speed.

Steady Power

Let's take the base case of steady power (P₁/P₂=1, so P_average=P₁=P₂) and no wind (w=0, so W₁=V₁=kP₁^1/3). The equation simplifies to

TotalTime/Distance = 1/(kP_average^1/3).  

The inverse of that is 

V_average = Distance/TotalTime = kP_average^1/3. 

As expected, when drag forces predominate, our speed varies as power to the 1/3rd.

No wind

For the case of no wind, the equations 'simplify' to give

P_average/P₂ = (1+(P₁/P₂)^2/3) / (1 + (P₁/P₂)^-1/3) 

As it turns out, for values of P₁/P₂ of interest, a distance-weighted P_average is a very good approximation of the time-weighted P_average. [P_average/P₂ = (P₁/P₂ +1)/2] when there is no wind.

That is shown graphically in the bottom curve below. The degradation in average speed is visible at all values of P₁/P₂ other than one, but it is almost insignificant. It suggests that steady pace is the best option in calm conditions.

Wind

Now let's looks at how many seconds we can save in a 40K race (20K into the wind and 20K with the wind) at a given ratio of P₁/P₂ and various wind speeds. This is shown in the graph below.

The bottom blue line is the case of no wind discussed above.

The next two curves compare two different P_averages in a 5 mph wind. Interestingly, the advantage of using a "P₁/P₂>1 strategy" decreases for stronger cyclists. The difference between speeds into the wind versus with the wind is less for the stronger cyclists, so they gain less from this strategy.

The top two curves are with a 10 mph wind. The strategy yields larger returns in windier conditions.

Conclusion

Having said all that, I conclude that the time savings suggested here are insignificant. The analysis ignores too many other variables and the savings are so small, that I would not implement this strategy myself. 

Other Thoughts on Pacing

I have followed Alex Dowsett in his quest to set the 1-hour record (he set it in 2020 but it has since broken by others). I recall one of his comments on pacing.  He said that during the first-30-minutes he focuses on his aero position (the k we talked about above). He has spent enough time in the wind tunnel that he knows what his optimal position is.  It is an unnatural position and takes some energy to maintain.  In the second-30-minutes his form degrades, and his power increases to maintain or increase his lap speed.  This might be a good strategy for a windy day.  Focus on aero position heading into the wind, then focus more on power output heading with the wind?

===================== 

Calculation Notes:

Unfortunately, these equations cannot be solved analytically. A wind speed, power ratio, and target P_average were chosen. A P₁ was guessed. That guess was used to calculate a TotalTime/Distance (EQ 1), which was used to calculate P_average (EQ 2). The difference between the target P_average and the calculated P_average was used to make a new guess of P₁. Usually convergence to <0.01% error occurred in less than 4 iterations.

Equations:

TotalTime/Distance = 1/V₁ + 1/V₂ = 1/(W₁-w) + 1/(W₂+w)  EQ 1

and

TotalTime x P_average = P₁t₁ +P₂t₂

[or TotalTime/Distance x P_average = P₁/V₁ + P₂/V₂]  EQ 2

where W₁ = kP₁^1/3 etc.

and V₁ = W₁ - w    and     V₂ = W₂ + w

The Revolutionary War Journal of Cadwallader Colden Jr.

The Journal of Cadwallader Colden during the Revolutionary War; A Transcription and Commentary, by Jay A. Campbell and Kieran J. O'Keefe is now available for purchase.

PURCHASE BOOK AT LULU.COM

This book is a valuable addition to the libraries of students of the Revolutionary War, especially those with a special interest in the loyalists of the Hudson Valley.

Who was Cadwallader Colden Jr? Colden was a 54-year-old gentleman farmer in the semi-frontier area west of the Hudson River at the start of the war.  His father of the same name had served as Lt. Governor (and twice as interim Governor) of the province for many administrations over a 16-year period. Too old to fight, and with too heavy a legacy to change his allegiance, the younger Cadwallader struggled with pen to explain his position with respect to independence while maintaining safety for his large family and assets.

Colden, born 1722, was of the same generation as the namesake of this blog, Joel Campbell (1735-1828).  They lived in the same area and undoubtedly were acquainted.  Joel Campbell shopped at Colden's store four times in 1768 (the only period from which a ledger survives). In the journal, Colden includes two letters he addressed to the Goodwill Church, a Presbyterian congregation where Joel's daughter, Jemima, would marry.

What is the Journal? The journal is a 208-page bound book written in the hand of Cadwallader Colden in the collection of the Huntington Library. It might be more accurately described as a “letter book.”  Most of the entries are copies of letters Colden sent or received.  The earliest is dated December 8, 1776 and the latest is dated April 12, 1779. The letters are written from several different locations. Colden was summoned, arrested, jailed, paroled, and banished.  These events and movements of the British army caused Colden to move about the state.

Why a transcription? A transcription of the original journal makes this first-hand account of life in the Hudson Valley more accessible to historians and genealogists.  The transcription allows full-text searches.

Why a commentary?  The commentaries added by the authors describe people mentioned in Colden's journal. Many of them are well-known men of history (John Jay, Gouverneur Morris, and George Clinton were all recipients of multiple letters from Colden). Colden also names his hosts in exile, family, and fellow prisoners. Locations where Colden was held and roads where he traveled are described.  His home at the time (built 1767) is preserved in ruins in Montgomery, New York. Several of the inns where he stayed under house-arrest are still preserved.

The paperback book is self-published and is only available by on-line purchase.

The Jonathan Campbell Branch on the Y-DNA Tree

BREAKING NEWS!

A branch on the patriarchal genetic tree has been confirmed to be that of Jonathan Campbell, born 1770 in New York.  The branch, which is synonymous with a Y-DNA mutation known as FTA92871, is unique to Jonathan and his male descendants. This mutation originated with Jonathan.  His father and brothers do not have it.

You can view the tree here:

https://www.familytreedna.com/public/y-dna-haplotree/R;name=R-FTA92871
When the page loads, click the right arrow to expose the branches.

The next branch down the tree has been identified as FTB16962.  This person is estimated to have lived around 1600.  He has not yet been identified.

If you are a descendant of Jonathan, here is your Campbell tree working into the past...

Jonathan 1770 - FTA92871
Joel ~1735
Samuel ~1700
Robert ~1660
Archibald ~1630
.
.
FTB16962 (Scotland)~1600
.
.
FTA93117 (Craignish Campbells) ~1370-1600  See Blog Christian Campbell - Abt 1350 - A Craignish Campbell
.
.
FTB13858 (Campbell Main Line) ~1150

Jonathan was too young to have fought in the Revolutionary War, but he certainly experienced many of its events in the Hudson Valley during its long duration, 1776-1783.  His older brothers and father undoubtedly shared war stories with him.  When he was 13 in 1783, he may have walked the short distance from his father's farm to New Windsor where Washington's Army was waiting for peace negotiations to be finalized. 

As a young man, he moved farther west to what would become Deerpark, New York.  There he owned property on a flood plain of the Neversink River called 'Campbell Flats' by the local surveyor. 

He moved again with extended family to the area where the Chemung River meets the Susquehanna near the NY/PA border. 

He raised a very large family (13 children?).  Ten of his descendants are part of the Campbell DNA Project and have been tested for Y-DNA markers including three that have been tested specifically for the FTA92871 polymorphism.

Maybe someone can write a book on this man who now has his own branch on the Y-DNA Haplotree.

Christian Campbell - Abt 1350 - A Craignish Campbell

My recent research has been focused on the Campbell paternal line. The breakthroughs in Y-DNA (see prior articles) have uncovered more deep ancestors.  

One such discovery is my link to the Craignish branch of the Campbells. The Craignish line started with the second son of a Campbell on the main (Argyll) line in about 1130.  Somewhere along the Craignish line, a non-inheriting son (or a bastard) started the branch to me.

My common ancestor on the Craignish line is estimated to be in the 1400-1600 period. Interestingly, the genealogy of Craignish is fairly well documented in this period. In 1720, one of the Craignish family put to manuscript the history as he had come to know it. It has been published as The Manuscript History of Craignish. (see link below)

One of the more interesting stories in his account (and one whose accuracy has been questioned) is the story of Christian, the daughter of Dugall Campbell of Craignish, who lived in about 1350. Just remember, if you are in the haplogroup FTA93117, you are related to these people.

This Dugall had no sons, so on his death, the clan lands would move to his brother, Malcolm, or to Malcolm's eldest son, Ronald. 

The deadly nature of family quarrels is illustrated by the story of Finguala, the sister of Dugall.  Finguala's husband had a quarrel with Dugall. The dispute led the husband to attempt an ambush of Dugall, which backfired, resulting in the death of Finguala's husband. (p 214).

The manuscript's author, Alexander Campbell (abt 1670-1725), referred to Dugall's daughter as "the Notorious Christian." [Note that this Alexander lived concurrently with my line's first American, Robert Campbell of Newark, NJ].

Christian married McDougal of Lorne and by him had a son. This son supposed that the Craignish lands were his inheritance and proceeded to demand rent from the inhabitants. Christian's cousin, Ronald (son of her father's brother), defended what he saw to be his inheritance.  In one of the skirmishes, Christian's son was killed.

After the death of her son and first husband, Christian married Alexander McNauchton.  Upon his death, she received a third of his Barony.

But Christian was not done.  She courted a younger Iver Campbell, head-servant of the Chief of Clan Campbell. By convincing him to "ly with her" in a wood near the Strath of Craignish and subsequently "happened to be with child", she obtained the Clan Chief's approval for her marriage. But the approval was at the price of signing over the deeds to the lands of her father to the Chief (which she had no right to do.) But who was to question the new owner, the Chief, the most powerful man in the Highlands?

Thus, Christian defrauded her cousin, Ronald, and his descendants (I guess that is sort of me) of their rightful inheritance.  It left a bitter taste in the mouths of Ronald's descendants for years to come.

The Manuscript History is here:  https://digital.nls.uk/scottish-history-society-publications/browse/archive/126513622