SCSPARTAN CODEMATH · Digital sextant← Navigation tools

MATH 4DAT / Live phone sextant

Find where you are.
From the sky.

Your phone can feel which way is down. Point its top edge at the North Star or the Sun, and it measures how high it is. Sailors used that same angle, plus a good clock, to find their way across oceans long before GPS.

  1. 1Flat means zero

    Lay the phone flat on a table, screen up, and tap “Zero the phone.” Do this once before every trip.

  2. 2Look along the top edge

    At night, hold the phone up by your eye and look along its top edge at the North Star, like looking down a straw. Both feet on the ground.

  3. 3Sun: never look up

    In the daytime, look DOWN at your other hand. Tip the phone until its shadow on your palm is a thin line. Now the top edge points at the Sun. Watch your hand, not the sky.

  4. 4Rest your elbows

    Lean your elbows on a wall, a rail, or a car roof. When the dot turns green, tap “Save this angle.” The app remembers the angle and the exact time.

  5. 5Read your answer

    North Star: one save is enough, and the angle is about how far north you are. Sun: save every 3 minutes around lunchtime until the Sun is clearly going back down. The app finds the highest point and tells you where you are.

Practice mode · move the slider to pretend to tilt the phone

—

Waiting for the sensor…

After the fixes: —

Get ready
Lay the phone flat on a table, screen up, then tap. Now flat really means 0°.
Saved angles (0)
Last saved angle, after the fixes—

Keep going! Save an angle every 3 minutes, starting about 20 minutes before lunchtime noon, until the Sun is clearly going back down.

The app fixes two small things: air bends starlight a little, and the Sun is a circle, not a dot.

Why does this work?

Latitude: how far north. At the North Pole, the North Star is straight overhead, at 90°. At the equator, it sits on the edge of the sky, at 0°. Everywhere in between, its height matches how far north you are.

Longitude: how far east or west. Earth spins all the way around once a day. So the Sun's highest moment comes 4 minutes later for every degree you go west. Compare your noon with noon in England and you know how far around the world you are.

Sailors did this first. For hundreds of years before GPS satellites, sailors used a tool called a sextant to measure these angles and a very good clock to know the time. Your phone can feel which way is down (gravity), so it can measure the same angles.

Small mistakes add up. Being off by just a tenth of a degree moves you about 7 miles on the map. That's why you hold still and save more than once.

Stay safe
  • Your eyes. Never look at the Sun — not with your eyes, not along the phone, not through sunglasses, not on the camera screen. Even a second can hurt. Let the shadow do the aiming.
  • Your feet. Sight from a spot where you can stand still. Don’t walk, lean over a rail, or stand near traffic or open water while you look up.
  • Your phone. This app never uses the camera. A phone left face-up in strong sun gets hot and shuts off, so keep it in the shade between saves.
  • Your position. Even a careful phone sight can be tens of miles off. This is for learning and for backup. Always carry a real map, compass, or GPS.
Troubleshooting

Something look wrong? Find your problem below. Each one says why it happens and how to fix it, with a true story from navigation history when there is one.

Phone problems

The number keeps jumping around.

Why: Hands always shake a little, and the motion sensor has a tiny bit of electrical fuzz too.

Fix: Rest your elbows on a railing, fence, or car roof. Breathe out slowly, wait for the green dot, then save. Save 3 to 5 angles so the app can average them.

From history: World War II bomber navigators had the same trouble with bubble sextants. Later models averaged the reading automatically, sampling every 2 seconds for 2 minutes.

Lying flat, the phone does not read 0°.

Why: Every phone's motion sensor has a small built-in error, often up to about 1°. It also shifts a little as the phone warms up. One degree is about 69 miles on the map!

Fix: Tap “Zero the phone” on a flat table before you start, and again after the phone has been in a warm pocket. Flip check: after zeroing, turn the phone around so the top points the other way. It should still read about 0°. If it doesn't, the table is tilted — zero on a flatter surface.

From history: A 2015 medical study found one iPhone read about 1.1° off until it was zeroed, and recommended a zeroing button — the same idea as a sextant's index correction.

A thick case or camera bump throws the angle off.

Why: The app measures the sensor inside the phone, not the edge you look along. A bump only 1 mm tall along a 15 cm phone tilts your aim by about 0.4° — around 25 miles. (This is an estimate from geometry.)

Fix: Take the phone out of a bulky case, and sight along a smooth, straight edge of the phone, not across the camera bump.

The angle is way off in a car or on a boat.

Why: When you speed up, slow down, turn, or rock on waves, the phone feels that push just like gravity. It can't tell them apart, so “down” looks tilted.

Fix: Stand still on solid ground when you can. On a boat, take many sights and average them, and expect bigger errors.

From history: Bubble sextants had exactly this problem. The Bowditch navigation manual lists typical errors of about 2 miles on land, 5–10 miles in steady flight, 10–16 miles on a gently rolling ship, and 30 miles or more in a moderate sea.

The website says there is no sensor, or it won't start.

Why: Browsers only share motion data with secure (https) pages. iPhones also ask for permission, and only after you tap a button. Most desktop and laptop computers have no motion sensor at all.

Fix: Open the page on your phone, tap “Use my phone’s sensor,” and choose Allow. If you tapped Don't Allow, turn motion access back on in your browser's website settings. The MATH 4DAT app itself needs no permission.

Sighting problems

My Sun answer is about 16 miles off.

Why: The Sun is a circle about half a degree wide. The shadow method points at its middle. A real sextant usually lines up its bottom edge. Picking the wrong one in the app adds or removes a quarter of a degree.

Fix: With the phone, choose “Sun (shadow method — aims at the middle).” Only choose a top-edge or bottom-edge option when you really lined up that edge with a sextant. Mixing up the top and bottom edges is a whole Sun-width off — about 32 miles.

My longitude is off but my latitude is fine.

Why: Longitude comes from time. Earth turns a quarter of a degree every minute, so a clock that is 1 minute wrong moves you about 15 miles east or west (near the equator). Every 4 seconds of error is about a mile.

Fix: The app uses your phone's clock, which is set by the network — keep it that way. Save angles on both sides of noon so the app can find the exact middle.

From history: In 1789, after the Bounty mutiny, William Bligh sailed an open boat 3,618 miles to Timor. When the only watch aboard stopped, he had to work out the time from noon sightings of the Sun. A century later Joshua Slocum sailed alone around the world with a cheap tin clock and checked his longitude with “lunar distances,” measuring the Moon against the stars.

At noon the Sun seems to stop moving.

Why: Near noon the Sun's height barely changes for several minutes, so it's hard to tell the exact top moment.

Fix: That's why the app wants saves before and after noon. It draws a smooth curve through all of them and finds the middle. Start about 20 minutes early and keep going until the Sun is clearly lower.

From history: The Bowditch manual warns that the Sun “hangs” at noon and recommends the same trick: time equal heights before and after noon and take the halfway time.

Sights close to the horizon give strange answers.

Why: Air bends light, and it bends it most near the horizon — about 5′ at 10° up and over half a degree at the horizon. Cold, heat, and weather change the bend.

Fix: Only use a star or Sun that is higher than about 15° — a fist and a half held at arm's length above the horizon.

I'm not sure I found the North Star.

Why: Many stars look alike, and the North Star is not the brightest star in the sky.

Fix: Find the Big Dipper. The two stars at the end of its cup point straight to the North Star. It's the star that stays put while the others slowly circle it.

From history: On his first voyage in 1492, Christopher Columbus measured the North Star with a quadrant and wrote down about 42° N while he was really near 21° N off Cuba. He blamed the instrument. One researcher thinks he read the wrong scale on it.

If you use a real sextant

Index error: the sextant doesn't read 0 on the horizon.

Why: The two mirrors aren't perfectly lined up, so every reading is a little too high or too low.

Fix: Set the arm to 0 and look at the horizon. Line the two images up and read the scale. Remember “if it's on, it's off”: a reading on the arc is subtracted, and a reading off the arc is added. The app's “Zero the phone” button does the same job.

The sextant wasn't held straight up and down.

Why: A tilted sextant measures to the wrong spot on the horizon and reads too high. Bowditch lists it first among common sextant errors.

Fix: “Rock the arc”: swing the sextant gently side to side. The Sun or star traces a little curve, and the lowest point of the curve is the right reading. The phone doesn't need this — rolling it around its top edge doesn't change the angle.

The mirrors or telescope are out of adjustment.

Why: There are three fixable errors besides index error: perpendicularity (index mirror tilted), side error (horizon glass tilted), and collimation (telescope crooked).

Fix: Adjust them in this order: perpendicularity, side error, collimation, then check index error last.

The sea horizon is hazy or looks wrong.

Why: A sea sextant measures up from the horizon. Haze, mirages, or a nearby shoreline can hide the true horizon, and warm or cold air over the water changes the “dip” correction.

Fix: Use a clear horizon, measure your height of eye carefully, and be suspicious of sights near fronts or mirages. The phone uses gravity instead of the horizon, so it has no dip — the same reason pilots used bubble sextants.

Lessons from history

Check your map and tools, not just your math.

Why: In 1707 a British fleet under Sir Cloudesley Shovell hit the Scilly Isles and between 1,400 and 2,000 sailors died.

What happened next: Historians point to several causes: charts that put the islands in the wrong place, faulty compasses, and uncertain position-finding. The disaster helped lead to the Longitude Act of 1714 and John Harrison's sea clocks.

Know how big your error might be — and plan for it.

Why: In 1916 Frank Worsley steered the tiny lifeboat James Caird about 800 miles from Elephant Island to South Georgia to save Shackleton's crew. Clouds and huge waves allowed only a handful of Sun sights, one taken through cloud by guessing the Sun's middle.

What happened next: Worsley averaged each series of sights, and because he wasn't sure within about 10 miles, he aimed deliberately at the island's west coast instead of trying to hit its tip. Aiming off on purpose is still taught today.

One sight gives a line, not a dot.

Why: In 1837 Captain Thomas Sumner discovered that a single Sun sight puts you somewhere on a line. In 1937 Amelia Earhart's last radio message said “We are on the line 157 337” — a line of position, but without a second sight or a landmark, no point on it.

What happened next: Get two or more lines that cross: the Sun at different times, two stars, or the North Star plus the noon Sun. Where they cross, you are.

Why learn this when phones have GPS?

Why: GPS signals are weak and can be jammed or faked, and a dead battery or broken receiver leaves you with nothing.

What happened next: In 2015 the U.S. Naval Academy started teaching celestial navigation again as a backup. The sky can't be switched off.

For grown-ups: the technical numbers
  • Raw altitude Hs — · spread ±—′
  • Observed altitude Ho — · refraction —′ · semi-diameter 0′ · index error 0′
  • Gravity is the horizon, so there is no dip correction, as with a bubble sextant. Rolling the phone about its top edge does not change the reading.
  • 0.1° = 6 nautical miles of position error. A 1-minute clock error moves longitude 15′.