Madogawa › Methods and limits
Methods and limits
Last updated: 16 Oct 2026
This page explains how Madogawa's answers are calculated and where they stop being reliable. Every "More" link on the answer card, the timeline, the map and the calendar leads here.
1. How left and right are decided
The track is divided into points every 100 m, and at each point we calculate the direction the train is heading (its bearing). When the difference between that heading and the direction of a landmark is between 20 and 160 degrees, the landmark is treated as being outside a window, and the sign of the difference tells us whether it is on the left or the right as you face forward. The two directions of each line (for example, toward Shin-Osaka and toward Tokyo on the Tokaido Shinkansen) are calculated separately, by actually tracing the track in each direction. We never take the result for one direction and simply mirror it.
Left and right here mean left and right as you sit facing the direction of travel. Seat numbers and letters are not used, because seat layouts differ by train and formation.
2. Line of sight
Using the GSI elevation tiles (DEM10B, roughly a 10 m grid), we check every 200 m whether any terrain rises above the straight line between the window and the landmark. The window is assumed to be 4 m above the track. We also run the calculation at 3 m and 5 m, and stretches where the result changes are marked as sensitive to eye height in the public data. The curvature of the Earth and atmospheric refraction (coefficient 7/6) are included.
Landmarks that would appear only a fraction of a degree above the horizon are dropped, because small terrain errors would flip the result. The minimum is 0.3 degrees for tall mountains and towers and 1.0 degree for everything else (lakes and seas usually lie below eye level, so this minimum is not used for them; they are labelled "Seen" only when enough travel records exist). Stretches where the clearance over the terrain is less than 10 m are flagged as grazing. Only lines of sight that continue for at least 300 m count as a stretch (the public data also keeps shorter fragments, but the tables and the tool do not use them).
Noise barriers, buildings, trees and cuttings are not in the calculation. For that reason, low features such as lakes and the sea are never labelled "Line of sight only" by calculation alone; they stay "Needs checking" until enough reports exist.
3. How labels are decided
Seen = 2+ independent reports from the train + line of sight by calculation / Line of sight only = line of sight by calculation, fewer than 2 reports / Needs checking = reported but no calculated line of sight, cannot be judged by calculation alone, or neither reported nor in calculated line of sight (lakes and seas labelled Seen are shown as "Seen (hidden by noise barriers in places)")
A report counts only when it contains a sentence, which we quote and store, saying the landmark can be seen from this line. A report whose destination or side shows the direction of travel counts for that direction, and a report that does not limit the direction counts once for each direction. Reports about other lines, conventional (non-Shinkansen) lines or the opposite direction do not count toward that direction.
4. Tunnels and viaducts
The height of the track is estimated by drawing upper and lower lines over the ground profile that never exceed a gradient limit assumed for each line. Where the ground is more than a set height above the estimated track (values for each line in the table below), we treat it as a tunnel; where the track is more than 5 m above the ground, we treat it as a viaduct. The gradient is an assumed value, so tunnel positions and lengths can differ from the real ones. The table below lists the estimated tunnel share for each line next to the published figure where we could confirm a source. For the Sanyo Shinkansen, the height difference treated as tunnel is set lower so that the estimate comes closer to the published figure.
| Line | Gradient limit (assumed) | Ground above track treated as tunnel | Estimated tunnel share | Published tunnel share |
|---|---|---|---|---|
| Tokaido Shinkansen | 15‰ | 25 m | 9.9% | No published figure for this line alone found |
| Sanyo Shinkansen | 15‰ | 15 m | 45.3% | 51% (source) |
| Hokuriku Shinkansen | 15‰ (Tokyo – Takasaki); 30‰ (Takasaki – Tsuruga) | 25 m | 25.4% | No published figure for this line alone found |
| Tohoku Shinkansen | 15‰ | 25 m | 21.3% | No published figure for this line alone found |
5. Passing times
The fastest published travel time for each line (see the table on Data and sources) is spread along the line in proportion to distance. Because stops shift the real passing times, even the fastest trains carry a margin of plus or minus 10 minutes, and times are rounded to 5 minutes. If you enter the arrival time of your train, the time is spread between your departure and arrival instead, and the margin becomes plus or minus 5 minutes. No timetables are reproduced.
6. Daylight and sunset
The height and direction of the sun are calculated with the method used by the US National Oceanic and Atmospheric Administration (based on Meeus). All times are Japan Standard Time (UTC+9) and do not depend on the time zone of your device. A sun height of 6 degrees or more is "Daylight", 6 to -0.833 degrees is "Low sun", -0.833 to -6 degrees is "Twilight", and anything lower is "Dark". The value -0.833 degrees is the standard sunrise and sunset threshold, which allows for refraction and the size of the sun's disc. When a time falls within the margin (plus or minus minutes) of a boundary, it is shown as "Borderline".
The seasonal calendar is calculated for the 1st, the 15th and the last day of each month, and cells where those three days differ are hatched. Not a weather forecast. Shows whether you would pass in daylight, based on sun elevation for a representative day each month and estimated travel time. Hatched cells change within the month.
7. Known limits
- Noise barriers, buildings, trees and cuttings are not in the calculation. Low features such as lakes, rivers and the sea may be hidden by barriers.
- Tunnel sections are estimated from terrain and may differ from the actual location and length.
- The route comes from data based on 1:25,000 maps and can be off by tens of metres.
- Window height, rolling stock and where you sit (window or aisle) change how much you can see.
- Clouds, haze, rain and other weather are not calculated.
- Ads shown on the pages have nothing to do with the site's results.
Frequently asked questions
- Should I sit on the same side for the return trip?
- No. The direction of travel is reversed, so left and right are reversed too. Enter the return section to get the answer calculated for that direction.
- What is the difference between "Line of sight only" and "Seen"?
- Both have a calculated line of sight. "Seen" also has at least two reports from the train that match the direction of travel.
- Will the train pass at exactly the time shown?
- No. It is an estimate made by spreading the travel time by distance, and it shifts with stops and operations. Entering your arrival time narrows the margin.
- What about rainy or cloudy days?
- Weather is not part of the calculation. The answers assume clear weather and an unobstructed view.
- Can you tell me which seat number to book?
- No. Seat layouts differ by train and formation, so please check the railway's official seat map.