UTM coordinates and knowing how to get the grid zone letter?

Question

I am using a framework called GeodeticUTMConverter to convert from decimal style coordinates to UTM. However the framework only provides the Northing, Easing, Grid Zone and Hemisphere, but not the grid zone letter.

If I have the following:

northing = 5067804.5036825798
easting = 551203.31329645123
gridZone = 10
hemisphere = kUTMHemisphereNorthern

The UTM would be 10T E 551203 N 5067804.

What is the most accurate way to calculate what the grid zone letter should be? How does the T get calculated?

EDIT: Added method that I wrote to calculate:

+ (NSString *)UTMlatZoneForCoordinates:(CLLocationCoordinate2D)coordinate {

    NSString *DigraphLetrsE = @"ABCDEFGHJKLMNPQRSTUVWXYZ";
    int latz = 0;//Latitude zone: A-B S of -80, C-W -80 to +72, X 72-84, Y,Z N of 84
    double latd = coordinate.latitude;

    if (latd > -80 && latd < 72) {
        latz = floor((latd + 80)/8)+2;
    }
    if (latd > 72 && latd < 84) {
        latz = 21;
    }
    if (latd > 84){
        latz = 23;
    }

    char letter = [DigraphLetrsE characterAtIndex:latz];
    return [NSString stringWithFormat:@"%c", letter];

}

Answer 1

"T" is a latitude band. To calculate the latitude band, you would have to unproject the UTM coordinates back to latitude-longitude first. A latitude band is 8 degrees north-south except the northernmost band which is from 72°N to 84°N. The southernmost band is "C" and starts at 80°S. The letters increase to X, but I and O are omitted.

You might think that you could figure out the Y / Northing ranges that correspond to the latitude bands, but to preserve conformality, latitude lines curve in transverse Mercator so there isn't a 1-to-1 relationship.

If data is in the polar regions, the UPS system is used instead, and the areas are divided into two halves: A and B and Y and Z and the stereographic projection is used instead.

Answer 2

The UTM system divides the Earth between 80°S and 84°N latitude into 60 zones, each 6° of longitude in width.

Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174° to 180° E.

Each longitude zone is segmented into 20 latitude bands.

Each latitude band is 8° high, and is lettered starting from "C" at 80°S, increasing up the English alphabet until "X", omitting the letters "I" and "O" (because of their similarity to the numerals one and zero). The last latitude band, "X", is extended an extra 4°, so it ends at 84°N latitude, thus covering the northernmost land on Earth.

For more info visit UTM