Maps & Flythrough

How this was custom-built: a GIS teaching artifact

The 19 stops

Public-domain originals from Wikimedia Commons and the New York Public Library. The cartographers who made these were the GPS engineers of their era. Their lines are how the Whydah found its way (and didn't).

Latitude lines run east-west around the globe. They tell you how far north or south you are from the equator. Longitude lines run north-south. They tell you how far east or west you are from a chosen starting line (the "prime meridian", since 1884 that's a line that runs through Greenwich, England).

Latitude is the easy one. Point a sextant or backstaff at the sun at noon (or at the North Star at night). Measure the angle. Look it up on a table. That's your latitude. Sailors had been doing this since the 1400s.

Longitude is a clock problem. The Earth spins 360 degrees in 24 hours, so every 15 degrees east or west equals one hour of time difference. To know your longitude, you need two clocks running at once: one for where you are now (easy: read the sun) and one for where you started from (hard: your starting clock has to keep perfect time on a rocking, salty, hot-and-cold ship for months).

In 1717 nobody had a clock that could pull this off. Sailors could find their latitude, but their longitude was a guess that got worse every day. The clock that finally solved it, John Harrison's H4, didn't prove itself until 1761, 44 years after the Whydah wrecked.

The math angle. Before chronometers existed, sailors used the lunar distance method to figure out time at sea: measure the angle between the Moon and a chosen star, then run a stack of trigonometric calculations to back out Greenwich time. The Science Museum London has a clear walkthrough (Where in the World? The Mathematics of Navigation). The almanac tables of predicted celestial positions were computed by hand, often by women and children working from home, who were called computers. The word "computer" originally meant a person who computes.

Compass centuries old by 1717

Magnetized needle on a pivot. Gave a coarse heading. Standard on all serious sea vessels.

Backstaff invented John Davis, 1594

The standard latitude tool of the 17th–early 18th century. Measured the sun's altitude from its shadow. User didn't look at the sun directly. This is what the Whydah's 16-year-old pilot John Julian would have used.

Mariner's astrolabe old tech, fading out by 1717

A medieval brass ring for reading the altitude of the sun or Polaris. By 1717 it was mostly obsolete at sea (the backstaff had replaced it over the previous decades), though older or poorer ships might still carry one. We include it to show how fast the toolkit was changing.

What DIDN't exist yet in 1717

Octant 1731, fourteen years too late

Hadley's reflecting octant. A small mirror let you see horizon and sun in the same eyepiece, faster and more accurate than the backstaff.

Sextant 1757

Wider arc than the octant (60 degrees vs 45) so it could measure lunar distances, the workaround for finding longitude before chronometers became affordable.

Marine chronometer (Harrison's H4) proved useful 1761, 44 years too late

The clock that solved longitude. Lost only ~5 seconds over an 81-day voyage. H5 (pictured) is the production-ready version Harrison built after H4 won the Longitude Prize.

You cannot flatten a globe onto a flat sheet of paper without stretching, squishing, or tearing something. Mathematicians proved this in the 1800s. Every world map you've ever seen is a trade-off: keep one thing accurate, give up another. The four things mapmakers can try to keep accurate are:

• Shape: countries look like the right shape, but their size gets distorted. Mercator does this. Good for navigation; bad for comparing how big places really are.
• Size: countries are the correct size relative to each other, but their shapes get squished. Mollweide, Goode, and Equal Earth do this. Good for showing where people live or where rainforests are; bad if you care what the country actually looks like.
• Distance: distances along certain lines are accurate. Useful if you want to know "how far is X from my city."
• Compromise: nothing is exactly right, but nothing is too far off either. Robinson and Winkel Tripel are compromise projections. National Geographic and the American Geographical Society use them for general world maps.

A French mathematician named Nicolas Tissot came up with a clever test in 1859: imagine a bunch of identical circles placed evenly across the globe. Now flatten the globe onto each kind of map and watch what happens to the circles. Where they stay round, the map kept the shape right. Where they balloon up or squish flat, the map is distorting size. You can see the trade-off.

Mercator's 1569 map was a tool for sailors, not a wall map for classrooms. It wasn't widely adopted for marine charts until the early 18th century. By 1717 it was becoming the working standard for ocean navigation. Its key feature: any straight line you draw on it is a course you can actually sail by holding one compass heading the whole way. A 1717 navigator could draw a straight line from Cape Cod to the Azores, read the compass direction off that line, and just hold that heading. Shorter routes exist (called "great circles"), but they require you to keep adjusting your compass heading as you go, hard to do without precise instruments.

Google Maps uses Web Mercator for the same reason a sailor did: zoom in on any neighborhood and a square block still looks like a square. The price is that Greenland looks gigantic when you zoom out. For street-level use, that's a fine trade.

Latitude was the findable one. Here's the trick a pilot like 16-year-old John Julian used.

The North Star shortcut: the angle from the horizon up to Polaris is (almost exactly) your latitude. Stand in Salem and Polaris sits about 42° above the horizon, because Salem is at 42°N.

Make a simple quadrant (10 min):

1. Tape a drinking straw along the flat edge of a protractor.
2. Tie a string with a small weight through the protractor's center hole.
3. Sight a star (or a far rooftop) through the straw; pinch the string where it crosses the scale.
4. Read the angle: 90° minus that reading = the object's height above the horizon.

At night: aim at Polaris: the height you read ≈ your latitude. Check it against Google Maps.
At noon: measure the sun's height (never look straight at it. Use a backstaff or read a shadow). Latitude = 90° − sun's height + the sun's declination for that date (your teacher has the table).

Why it matters: there was no equivalent trick for longitude. That's why the Whydah could find how far north they were but not how far west they'd drifted in the dark, and why she grounded at Wellfleet.

Dead reckoning = figure out where you are from where you started, plus your heading, speed, and time. (1 knot = 1 nautical mile per hour.)

Worked example: you leave port steering northeast (045°) at 5 knots. After 6 hours you've sailed 5 × 6 = 30 nautical miles along 045°. Draw that line on the plotting grid. The far end is your best guess at "you are here."

Do it: plot Bellamy's Jamaica→Carolinas run leg by leg. Each leg has a heading, a speed, and a number of hours. Chain them across the grid.

Now break it: a current quietly pushes you 10 miles west and you never notice. Re-mark where you think you are vs. where you really are. That gap is dead-reckoning error. And it grew every day at sea.

Journal it: this is the S14 voyage-plan entry. The error you just drew, plus no way to fix longitude, plus a night nor'easter = the wreck.

Every place on Earth has an address: latitude (how far N/S of the equator) and longitude (how far E/W of Greenwich). Order is always lat, then long.

Warm-up: say these in plain words, then plot them on the blank lat/long grid:

• The wreck site: 41.891°N, 69.957°W (off Marconi Beach, Wellfleet)
• Boston Court House (the trial): ~42.359°N, 71.058°W
• Your school: right-click it in Google Maps to read the coordinates

GIS note: computers store these as numbers, with N and E positive, S and W negative. So the wreck is (41.891, -69.957). That sign flip is how a map app tells west from east.

Why it matters: every stop on the 3D flythrough is a real coordinate. Turning a place into a pair of numbers is the first move in all of GIS.

This is the GIS heart of the whole unit. In 1717 Cyprian Southack marked the wreck on his hand-drawn chart. His own mark was the label "Pirate Ship Whido lost" (the famous red X on reproductions was added later). In 1984 Barry Clifford had to answer: where does that mark land in real-world coordinates?

Georeferencing is the answer. You pick a few features you can recognize on both the old map and a modern one (a point of land, a river mouth, a harbor). Match them up (those are control points), and the whole old map stretches into place over the real world. Now the X has a latitude and longitude.

Do it: open Southack's 1717 chart (earlier on this page) beside Google Earth. Find 3 shore features that appear on both. Read the modern coordinates of each, then estimate where Southack's wreck label lands today. You've just georeferenced a 300-year-old map.

Then the grid: Clifford searched the seabed in a numbered grid of squares. A grid of squares, each holding a value, is exactly how GIS stores a raster (like a satellite image). The S13 grid-archaeology activity is you doing the same thing.

Vocab: georeferencing · control point · raster / grid · layer

What's the shortest way across an ocean? On a globe it's a great circle. But on a flat Mercator map that shortest path looks like a curve, while a dead-straight line on Mercator (a rhumb line, one constant compass heading) is actually longer.

See it: stretch a string between Boston and London on a globe. It bows up over Greenland. Now draw the straight Boston–London line on a Mercator world map. Different paths, same two cities. (Or use the Great Circle Mapper.)

The 1717 choice: Bellamy held rhumb lines: one steady heading he could actually steer. A great circle means constantly re-adjusting your heading, which needs instruments he didn't have. Modern jets and ships fly great circles because GPS makes the adjusting easy.

Why it matters: the "best" route depends on your tools. Same ocean, different answer in 1717 and today.