Winter running at 51° N versus 34° S.

Daylight sets the schedule before pace does

Most winter running advice starts with the pace: slow down, run by feel, expect the cold to cost you something. That is fine as far as it goes, but the first question for a runner with a job and a calendar is simpler. When is it light? A great pace range is no help if the only free hour is forty minutes after sunset.

This guide works one runner through the same December in two places, 51 degrees north and 34 degrees south. The runner is the same, the easy pace is the same and the run is the same 8 km. Only the latitude, the date and the forecast change. By the end you will have a daylight window for each place, a dark-run check for four different start times, a pace range built from a rule table you can edit, and a layer list chosen by comfort rather than by a rule of thumb. Every number can be repeated in the cold weather run planner.

• The sunrise equation
• The runner
• 51° N
• 34° S
• Same run, two places
• Solar time or clock
• Pace for the cold
• Layers
• A week

The sunrise equation, in plain steps

Sunrise and sunset are not looked up. They are calculated from two inputs, the date and the latitude, and the calculation has been the same for decades. The planner runs it in your browser. In outline:

1. Count days. Turn the date into a day number counted from the year 2000.
2. Place the Earth in its orbit. The day number gives the sun's mean anomaly, and a small correction for the orbit's shape gives its true position along the ecliptic.
3. Find the tilt for the day. From that position comes the sun's declination, which is how far north or south of the equator it sits. It is about -23.4 degrees at the December solstice and +23.4 degrees in June.
4. Get the hour angle. For your latitude and that declination, the hour angle says how far the sun travels either side of solar noon before it reaches the horizon.
5. Convert angle to minutes. The sun moves 15 degrees an hour, so each degree of hour angle is four minutes. Subtract from solar noon for sunrise and add for sunset.

Two thresholds matter. Sunrise and sunset use a sun position of -0.833 degrees, which allows for the width of the sun's disc and the bending of light in the air. Civil twilight uses -6 degrees. Between civil dawn and sunrise the sky is already bright, and the same happens in reverse after sunset. The planner lists both so you can see the grey light around each short day, but it treats sunrise and sunset as the edges of daylight for its dark-run check.

The runner and the run

Meet a runner whose usual easy pace is 5:45 per km. They want an 8 km easy run on a weekday and can choose between four start times: 06:30 before work, 12:00 at lunch, 15:10 at the end of a short shift, or 17:30 after work. The same plan goes to both latitudes, 51 degrees north and 34 degrees south, using 21 December, the solstice, as the test date.

The forecasts differ, and so does what the rule table does with them.

Solar time keeps the comparison honest. Clocks add time zones and summer time, which are conventions rather than sunlight, so the table above puts both runners on the same footing. A later section shows what changes when you switch to your own clock.

51° N: a window that shrinks to under eight hours

Here are four dates at 51 degrees north. Day length is sunset minus sunrise, and the last column shows civil dawn and civil dusk.

On 1 November the runner has 9h 44m of daylight. By 21 December that has fallen to 7h 54m, a loss of 1 h 50 min, and the window runs from 08:03 to 15:57. The solstice is the low point. By 31 January the window has grown back to 9h 08m, 1 h 14 min longer than the shortest day, with sunrise at 07:26.

Civil twilight adds roughly forty minutes at each end on 21 December. The sky is bright from 07:23 and stays bright until 16:37. That helps with mood and with planning, but the planner does not treat twilight as daylight. If your run starts in twilight it says so, and it gives the civil dawn time next to the sunrise time so you can decide for yourself how you want to use that margin.

For this runner the useful window on the shortest day is the 7h 54m between 08:03 and 15:57. A run of under an hour fits easily inside it, and the question is simply which part of the day you can give it.

34° S: the same dates in summer

The southern runner is in the other half of the calendar. Same dates, same method, opposite season.

On 21 December the window at 34 degrees south is 14h 26m, from 04:47 to 19:13. That is 6 h 32 min longer than the northern runner has on the same date. Between 1 November and the solstice the southern window grows by 58 min, and by 31 January it has eased back to 13h 46m.

The planning question flips. The northern runner asks where in a short day the run can go. The southern runner is rarely short of light, so the question becomes whether a very early start is really needed, since sunrise is at 04:47 and civil dawn at 04:18. A 06:30 run here begins 1 h 43 min after sunrise.

The same run in both places

Now the dark-run check. The finish time comes from the start time plus the run length. For the northern runner the forecast pushes the pace range to 5:55 to 6:13 per km (the next section shows why), so the check uses the slow end, which makes the 8 km run 50 minutes. The southern forecast adds nothing, so the run takes 46 minutes at 5:45 per km.

The result is stark. At 51 degrees north only the lunchtime run is in daylight on 21 December. The 06:30 start is more than an hour before sunrise, and the 15:10 and 17:30 starts finish after sunset. At 34 degrees south all four starts are in daylight, and the latest of them still finishes 57 min before sunset.

Look at the 15:10 row more closely, because it shows why the planner uses the slow end of the range. At the plain 5:45 pace the northern run would take 46 minutes and end at 15:56, which is 1 min before the 15:57 sunset. At the slow end of the weather-adjusted range it takes 50 minutes and ends at 16:00, 3 min after sunset. A small change in pace flips a daylight run into a dark one, and that is exactly the case where you want to be told before you leave the house.

Solar time, or your clock

Everything so far is in solar time. Your phone shows clock time, and the two can be very different. Take Sydney, which sits near 34 degrees south at longitude 151.2 east and keeps summer time at UTC+11 in December. On 21 December the planner gives 05:41 sunrise and 20:05 sunset on the clock, against 04:47 and 19:13 in solar time. That is a gap of 54 min. Summer time accounts for an hour. The few minutes in the other direction come from Sydney sitting slightly east of the meridian its standard time is based on, plus the sun's seasonal drift against the clock.

London shows the same effect on a smaller scale. On the clock at longitude 0.13 west and UTC+0 the solstice window is 08:04 to 15:53, almost the same as the 08:03 to 15:57 solar figures, because London is close to the middle of its zone.

Clock time also explains a puzzle that catches many winter runners. The shortest day is 21 December, but the earliest sunset is not. On a London clock sunset reaches its earliest value of 15:52 around 8 Dec and stays there until about 19 Dec, well before the solstice. Sunrise keeps getting later, reaching 08:06 between 26 Dec and 4 Jan. Evenings brighten first and mornings last, which is worth knowing if you are timing a run for the end of the working day in the second half of December.

The planner covers both cases. Type a latitude alone for solar time. Pick one of the 40 cities, or add a longitude and UTC offset yourself, for times on your clock.

Pace for the cold: a rule table you can edit

The planner does not try to predict your time. It starts from the easy pace you gave it and adds a range of percentages drawn from a short table. Each factor has its own row, the rows add together, and a run-type share scales the total. Here are the northern runner's three rows, using the starting values in the planner.

Applied to 5:45 per km, 3% gives 345 x 1.03 = 355.35, which rounds to 5:55, and 8% gives 345 x 1.08 = 372.60, which rounds to 6:13. The planner shows 5:55 to 6:13 per km. An 8 km run at the slow end is 8 x 373 = 2984 seconds, or 50 minutes after rounding.

Because the table is yours, none of these percentages are fixed. A runner who barely slows on wet roads can set the surface row to 0 and 1. A runner who loses more on ice can raise it. Intervals use a 50% share by default because the pace of the reps is set by effort and rep time, so only half of the adjustment is applied, which suits the warm-up and recovery jogs. Any edit changes the range at once, goes into the link you copy and appears on the printed sheet. A reset button restores the starting values.

One edge case deserves a sentence. If the forecast is exactly -5 °C, the band that starts at -5 applies, not the one above it. The same rule holds at 0, 5 and 10 degrees and at every wind band, so a number on an edge never falls between two rows. Wind of exactly 0 adds nothing at all and leaves the feels-like figure equal to the air temperature. For the southern runner at 18 °C with 8 km/h wind on a dry road the rows are 0% each, so the range collapses to 5:45 per km, the pace the runner started with.

Layers, chosen by your own comfort band

Layer advice usually comes as a single table that assumes you are an average runner. The planner asks you instead. Pick the comfort band that matches how you feel in the first ten minutes, and it shifts the temperature it uses to choose clothes.

The feels-like figure comes from the air temperature and the wind speed with a standard wind-chill formula. For -2 °C with 15 km/h wind it gives -6.9 °C. The comfort band then moves that figure.

A runner in the middle gets a thermal long-sleeve base, a fleece or insulating top, a windproof jacket, thermal tights, mittens or gloves with liners, a hat and a neck tube, thick socks. The runner who runs warm drops to the row above, which swaps the insulating top for a light fleece or second long-sleeve top, and the mittens for warm gloves. Every item is a tick box, on screen and on the printed sheet. When any run in your seven-day strip touches the dark, the list adds a head torch and reflective strips. On snow or ice it adds traction spikes for your shoes. In the wet it adds dry socks and a towel for afterwards.

The southern runner at 18 °C lands in the top row, which is a singlet or short-sleeve top, shorts, light socks and a cap.

Turning it into a week

1. Choose the place. Pick a city or type a latitude. For clock times add a longitude and UTC offset.
2. Set the dates. The seven-day strip shows the first seven of them. The table below it lists every date, up to 92.
3. Enter the run. Start time, distance, easy pace per km or per mile, and the run type.
4. Enter the forecast. Temperature, wind, surface and comfort band. Wind of 0 is fine.
5. Read the strip. Each day shows the daylight window, the run window, the pace range and a flag if the run touches the dark. Change a day to long, intervals or rest and the check updates.
6. Print or save. The printed sheet fits A4 or Letter. The CSV holds every date, ready for a spreadsheet.

If you run in miles, switch the pace unit and the distance box follows. The rule tables stay in percentages, so they work unchanged.

And at the far ends of the globe the planner says what is happening rather than guessing. At 80 degrees north on 21 December the sun does not rise, and the dates show as polar night with the twilight window if there is one. At 80 degrees south the sun does not set, and every run time counts as daylight.