This car looks fast:

First things first, that car doesn't look fast at all. You may wish to learn more about cars.
Secondly, your analogy is entirely fallacious. The appearance of the Earth may be judged by looking at the Earth. The speed at which it may or may not be moving through space can not, neither can its temperature. For your argument to be analogous, you'd have to uphold that the car is not mostly cyan and orange, that it does not have >= 2 wheels, or that it does not have the number "36" written on at least one of its doors.
IF the car DOESN'T go fast, it doesn't mean it CAN'T GO fast. :-)
But if something just "looks like duck" it isn't enough.
It has to "walk like duck" and "quack like duck" as well.
On short distances Earth "looks like duck (flat)", but it doesn't "walk like flat and quack like flat".
When you measure, you see it to be curved.
GPS is introduced just recently. Before that every travel was dependant on navigation by sun and stars.
Navigators, just like astronomers, knew stars and constellations very well.
GPS is reason why less people buy sextants, or only have it "just in case".
Some don't care. If they lose GPS, they will use radio. So, price of sextants went down.
You can buy marine sextant here:
http://www.ebay.com/bhp/marine-sextantPrices can be as low as $22, or as high as $600 or more.
You can easily learn how to use it. Google for it. You will also need some practice.
You can read astronomical data on numerous web sites.
If data is wrong anyone who can measure anything would gladly expose it.
Also, if someone falsely "expose" something, others will happily correct them.
So, I believe you can trust the data there, but if you don't, you can have your own sextant and check it out.
Prices given above show that virtually anyone can.
People bragging about being investigative (zetetic) give me confidence that they would do it.
Earth on short distances look flat. Yes? No?
It is "yes", or Flat Earthers wouldn't use it as "proof".
But navigators were covering long distances as well.
Distances much greater than plane sailing approximation can satisfy.
For shorter distances between Greek islands error of 1/2 mile is acceptable, because
your destination will still be in the view with or without such error.
But acros the Atlantic, and later Pacific, plane sailing will give much biggere error and you
won't come close enough to have known area around your destination within your view.
You would have to be more precise than that.
By using sextant navigators measured degrees of latitude.
They measured angles of well known stars and calculated position.
If that was inaccurate they wouldn't be able to travel accurately, not to speak of safe world circumnavigation.
Pacific ocean is almost half of Earth's surface. You have to be VERY precise to reach desired island.
With poor navigation you easily get lost.
To convert degrees into distances easier they defined nautical mile.
One nautical mile is distance between two verticals with angle between them of exactly ONE ARCMINUTE.It is 1852 meters.
That way to travel one degree you go exactly 60 nautical miles.
If at one place you measure 5° 14' more or less than another, their distance is 5x60 + 14 = 314 nautical miles.
(Ofcourse, you measure "horizontal" and "vertical" angular distances and just calculate linear distance using non-Euclidean Pythagoras.)
As we can see, Earth "looks like duck", but doesn't "walk like duck", nor "quack like duck".If you don't believe it, find long road
going north-south, measure 1852 meters segment, and then measure angle of Polaris from each end.
Mark the diference.
If the Earth was flat, your angular difference will vary with your distance from North pole.
At 1000 miles from North pole, the difference is 1.92 arcminutes.
At 3000 miles from North pole, the diference is 1.006 arcminutes.
At 5000 miles from North pole, the difference is 0.6 arcminutes.
If the Earth was globe your measurement would be independent of your location.
Navigators traveled all over and everywhere one nautical mile is ONE ARCMINUTE.
If it wasn't, if it was variable, who would care to even think of accepting nautical mile as distance unit?