If the Starship Enterprise dipped into the Earth’s atmosphere at a sub-warp speed, would we see it? And if the craft were visible, would it look like the object we’re familiar with from TV, with its saucer section and two nacelles? Well, if the Enterprise were travelling fast enough, then – bright physicists that we are – we’d expect the craft to experience the length contraction dictated by special relativity.According to this famous principle, a body moving relative to an observer will appear slightly shorter in the direction the body’s travelling in. Specifically, its observed length will have been reduced by the Lorentz factor (1–v2/c2)1/2, where v is the relative velocity of the moving object and c is the speed of light in a vacuum. However, the Enterprise won’t be seen as shorter despite zipping along so fast. In fact, it will appear to be the same length, but rotated.You might not have heard of this phenomenon before, but it’s often called the “Terrell effect” or “Terrell rotation”. It’s named after James Terrell – a physicist at the Los Alamos National Laboratory in the US, who first came up with the idea in 1957. The apparent rotation of an object moving near the speed of light is, in essence, a consequence of the time it takes light rays to travel from various points on the moving body to an observer’s eyes.
You can read the rest of the explanation and graphics in the article. Again, this is not to say that your "pole-in-barn" exercise that you did in relativity lessons is not valid. It is just that in that case, you were not asked what you actually SEE with your eyes when that pole is passing through the barn, and that your pole is long and thin, as opposed to an object with a substantial size and width. The notion that such object will be seen with our eyes flat as a pancake is arguably may not be true here.