We've discussed if spells travel in a straight line and about blocking spells. We know spells don't just happen. They have to be directed by a wand and they can be blocked, so there's every indication that most attack spells travel from the end of a wand to the object in question.
Is there anything to indicate how fast a projectile-style spell travels?
Answer
Well, from the books we know that when wizards duel (like in the dueling league) they face each other at a range where normal spoken communication is easy.
Beyond ~30 feet, you have to put in a lot more effort to be heard, which the books do not demonstrate happening - Harry and Draco, for example, exchanged threats just fine.
Therefore, we can assume that it is reasonable for an experienced duelist to react to their opponent's spell at a distance of ~30 feet.
The casting time of a spell seems to average around one second (verbal and motion casting). We can further assume that the common attack spells in duels can be distinguished by an experienced duelist from the first motion (so within a half second of the start of casting).
This leaves the opponent a half second to choose a defense and cast it before the spell is headed their way. They need to then cast their defense or counterattack, which will take approximately a second.
- At time 0 the attacker (A) begins casting a spell.
- At time 0.5, the defender (D) begins casting a defense or counter.
- At time 1, A's spell launches towards D. D still needs a half second to finish casting.
Therefore, if the spell can cover 30 feet in half a second, D will never be able to counter, and the duel will likely end with the first spell every time.
Spells can't move too slowly, either, or even an inexperienced duelist will have plenty of time to summon a defense - attacking will never hit.
I would therefore estimate that the spell takes between .75 and 1 second to travel a distance of up to 30 feet.
That works out to ~37.5 feet per second to 30 feet per second (I would expect that different spells travel at different speeds, but this works for an average range). This is fast, but not so fast that a prepared defender won't have time to defend himself and/or dodge.
For comparison, a quick google search suggests that most bullets from a handgun travel at a minimum of 1,000 feet per second (up to around 1,500 fps) when they exit the barrel. A spell travels, then, at ~2% the speed of a handgun bullet (rifle bullets are considerably faster).
These are back-of-the-envelope calculations, and may be off by a factor of two or three (if duelists stand 40 or even 60 feet apart, instead of 30). Even a worst-case scenario, though (60 feet apart, at which distance you MUST yell to be heard) has a spell traveling at less than 80 feet per second.
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