Deer Creek-advice

If you can, pick up your race packet on Saturday.

Also the two hills are pretty steep but if you did well on the hill with the cows in the Delaware TRI and you can take the alum creek hill ok, you will be fine.  I planned on walking up the final hill but ended up biking up it during the TRI @ deer creek.

Other than that, the bike course is like a frekin' nascar track.  Straights and left turns!

HA!  Except that he is hawt enought that noone would complaine if he ran around nekkid.

On Earth, the length of an arcdegree of north–south latitude difference, , is about 60 nautical miles, 111 kilometres or 69 statute miles at any latitude. The length of an arcdegree of east-west longitude difference, , is about the same at the equator as the north-south, reducing to zero at the poles.

In the case of a spheroid, a meridian and its anti-meridian form an ellipse, from which an exact expression for the length of an arcdegree of latitude difference is:

This radius of arc (or "arcradius") is in the plane of a meridian, and is known as the meridional radius of curvature, .^[2][3]

Similarly, an exact expression for the length of an arcdegree of longitude difference is:

The arcradius contained here is in the plane of the prime vertical, the east-west plane perpendicular (or "normal") to both the plane of the meridian and the plane tangent to the surface of the ellipsoid, and is known as the normal radius of curvature, .^[2][3]

Along the equator (east-west), equals the equatorial radius. The radius of curvature at a right angle to the equator (north-south), , is 43 km shorter, hence the length of an arcdegree of latitude difference at the equator is about 1 km less than the length of an arcdegree of longitude difference at the equator. The radii of curvature are equal at the poles where they are about 64 km greater than the north-south equatorial radius of curvature because the polar radius is 21 km less than the equatorial radius. The shorter polar radii indicate that the northern and southern hemispheres are flatter, making their radii of curvature longer. This flattening also 'pinches' the north-south equatorial radius of curvature, making it 43 km less than the equatorial radius. Both radii of curvature are perpendicular to the plane tangent to the surface of the ellipsoid at all latitudes, directed toward a point on the polar axis in the opposite hemisphere (except at the equator where both point toward Earth's center). The east-west radius of curvature reaches the axis, whereas the north-south radius of curvature is shorter at all latitudes except the poles.

The WGS84 ellipsoid, used by all GPS devices, uses an equatorial radius of 6378137.0 m and an inverse flattening, (1/f), of 298.257223563, hence its polar radius is 6356752.3142 m and its first eccentricity squared is 0.00669437999014.^[4] The more recent but little used IERS 2003 ellipsoid provides equatorial and polar radii of 6378136.6 and 6356751.9 m, respectively, and an inverse flattening of 298.25642.^[5] Lengths of degrees on the WGS84 and IERS 2003 ellipsoids are the same when rounded to six significant digits. An appropriate calculator for any latitude is provided by the U.S. government's National Geospatial-Intelligence Agency (NGA).^[6]

Latitude	N-S radius of curvature	Surface distance per 1° change in latitude		E-W radius of curvature	Surface distance per 1° change in longitude
0°	6335.44 km	110.574 km		6378.14 km	111.320 km
15°	6339.70 km	110.649 km		6379.57 km	107.551 km
30°	6351.38 km	110.852 km		6383.48 km	96.486 km
45°	6367.38 km	111.132 km		6388.84 km	78.847 km
60°	6383.45 km	111.412 km		6394.21 km	55.800 km
75°	6395.26 km	111.618 km		6398.15 km	28.902 km
90°	6399.59 km	111.694 km		6399.59 km	0.000 km

[edit] Types of latitude

With a spheroid that is slightly flattened by its rotation, cartographers refer to a variety of auxiliary latitudes to precisely adapt spherical projections according to their purpose.
For planets other than Earth, such as Mars, geographic and geocentric latitude are called "planetographic" and "planetocentric" latitude, respectively. Most maps of Mars since 2002 use planetocentric coordinates.

[edit] Common "latitude"

In common usage, "latitude" refers to geodetic or geographic latitude and is the angle between the equatorial plane and a line that is normal to the reference ellipsoid, which approximates the shape of Earth to account for flattening of the poles and bulging of the equator. This value usually differs from the geocentric latitude.

The expressions following assume elliptical polar sections and that all sections parallel to the equatorial plane are circular. Geographic latitude (with longitude) then provides a Gauss map. As defined earlier in this article, is the angular eccentricity of a meridian.

[edit] Reduced latitude

• On a spheroid, lines of reduced or parametric latitude, , form circles whose radii are the same as the radii of circles formed by the corresponding lines of latitude on a sphere with radius equal to the equatorial radius of the spheroid.

[edit] Authalic latitude

• Authalic latitude, , gives an area-preserving transform to the sphere.

[edit] Rectifying latitude

• Rectifying latitude, , is the surface distance from the equator, scaled so the pole is 90°, but involves elliptic integration:

[edit] Conformal latitude

• Conformal latitude, , gives an angle-preserving (conformal) transform to the sphere.

[edit] Geocentric latitude

• The geocentric latitude, , is the angle between the equatorial plane and a line from the center of Earth.

It is the size of the central angle between the equator and the point of interest, as measured along a meridian. This value usually differs from the geographic latitude, as so:

Illustration of geographic and geocentric latitudes.

[edit] Astronomical latitude

A more obscure measure of latitude is the astronomical latitude, which is the angle between the equatorial plane and the normal to the geoid (ie a plumb line). It originated as the angle between horizon and pole star. It differs from the geodetic latitude only slightly, due to the slight deviations of the geoid from the reference ellipsoid.

Astronomical latitude is not to be confused with declination, the coordinate astronomers use to describe the locations of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to describe the locations of stars north/south of the ecliptic (see ecliptic coordinates).

[edit] Palaeolatitude

Continents move over time, due to continental drift, taking whatever fossils and other features of interest they may have with them. Particularly when discussing fossils, it's often more useful to know where the fossil was when it was laid down, than where it is when it was dug up: this is called the palæolatitude of the fossil. The Palæolatitude can be constrained by palæomagnetic data. If tiny magnetisable grains are present when the rock is being formed, these will align themselves with Earth's magnetic field like compass needles. A magnetometer can deduce the orientation of these grains by subjecting a sample to a magnetic field, and the magnetic declination of the grains can be used to infer the latitude of deposition.

[edit] Comparison of selected types

The following plot shows the differences between the types of latitude. The data used are found in the table following the plot. Please note that the values in the table are in minutes, not degrees, and the plot reflects this as well. Also observe that the conformal symbols are hidden behind the geocentric due to being very close in value. Finally it is important to mention also that these differences don't mean that the use of one specific latitude will necessarily cause more distortions than the other (the real fact is that each latitude type is optimized for achieving a different goal).

Approximate difference from geographic latitude ("Lat")
Lat	Reduced	Authalic	Rectifying	Conformal	Geocentric
0°	0.00′	0.00′	0.00′	0.00′	0.00′
5°	1.01′	1.35′	1.52′	2.02′	2.02′
10°	1.99′	2.66′	2.99′	3.98′	3.98′
15°	2.91′	3.89′	4.37′	5.82′	5.82′
20°	3.75′	5.00′	5.62′	7.48′	7.48′
25°	4.47′	5.96′	6.70′	8.92′	8.92′
30°	5.05′	6.73′	7.57′	10.09′	10.09′
35°	5.48′	7.31′	8.22′	10.95′	10.96′
40°	5.75′	7.66′	8.62′	11.48′	11.49′
45°	5.84′	7.78′	8.76′	11.67′	11.67′
50°	5.75′	7.67′	8.63′	11.50′	11.50′
55°	5.49′	7.32′	8.23′	10.97′	10.98′
60°	5.06′	6.75′	7.59′	10.12′	10.13′
65°	4.48′	5.97′	6.72′	8.95′	8.96′
70°	3.76′	5.01′	5.64′	7.52′	7.52′
75°	2.92′	3.90′	4.39′	5.85′	5.85′
80°	2.00′	2.67′	3.00′	4.00′	4.01′
85°	1.02′	1.35′	1.52′	2.03′	2.03′
90°	0.00′	0.00′	0.00′	0.00′	0.00′

[edit] Corrections for altitude

Line IH is normal to the spheroid representing the Earth (colored orange) at point H. The angle it forms with the equator (represented by line CA) corresponds to the point's geodetic latitude.

When converting from geodetic ("common") latitude to other types of latitude, corrections must be made for altitude for systems which do not measure the angle from the normal of the spheroid. For example, in the figure at right, point H (located on the surface of the spheroid) and point H' (located at some greater elevation) have different geocentric latitudes (angles β and γ respectively), even though they share the same geodetic latitude (angle α). Note that the flatness of the spheroid and elevation of point H' in the image is significantly greater than what is found on the Earth, exaggerating the errors inherent in such calculations if left uncorrected. Note also that the reference ellipsoid used in the geodetic system is itself just an approximation of the true geoid, and therefore introduces its own errors, though the differences are less severe. (See Astronomical latitude, above.)