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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?
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.
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.
Jeff’s post got me thinking, and I thought the results of my research would be appreciated. Enjoy.
MythBusters, when testing “Never Bring a Knife to a Gunfight,” determined that somewhere between 20-16 feet, a person with a knife can run up and stab a person with a handgun before they can draw and fire.
A UK news article claims your average male can jog 8.3 miles per hour (about 12.173333333333 feet per second).
S(T) = D Can be used to determine Distance traveled (D), given Speed(S) and Time(T). To get Time we divide both sides by S, which gives us T=D/(S). So let’s plug and chug.
20 feet (12.173333333333 feet/second) ≈ 1.6429353778751 seconds
and
16 feet /(12.173333333333 feet/second) ≈ 1.3143483023001 seconds.
So using Jamie and Adam as our baseline, and assuming casting a spell takes the same time as drawing, cocking and firing a handgun, we have a window of about 1.3143483023001–1.6429353778751 seconds for our response times (for those of you who were wondering that is a gap of 0.3285870755750 seconds or about 1/3 second).
Mr Jeff said,
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.
Using the distance provided by Mr Jeff, that means our curse has (1.3143483023001–1.6429353778751) seconds to travel 30 feet, and hit the corresponding counter curse. Let’s pull up our formula again.
S(T) = D ⇒ S = D/(T) ⇒ D/(T) = S
Let’s plug and chug. 30 feet/(1.3143483023001 seconds) = 22.825 feet/second and 30 feet/(1.6429353778751 seconds) = 18.26 feet/second.
So our spells are traveling somewhere between 18.26 and 22.825 feet per second, or 12.45–15.5625 miles per hour.
That feels slow to me. I mean, it is faster than I can run, but it sounds quite a bit slower than Mr Jeff’s answer.
It might not be fair to compare Jamie and Adam’s reaction times to the reaction times of your average Wizard. After all, wizards in the Harry Potter world spend seven years learning to identify and cast spells. Yes, very few of their classes are taught in battlefield conditions (I’m looking at you Lockhart’s Pixies), but seven years of schooling is a lot of practice. Assuming a 180 day school year (the most common legal minimum in the United States of America) with 8 hours in class a day, times Seven years, 7(180)(8) = 10,080. There is the popular adage “It takes 10,000 hours to become a master.” Admittedly some of these classes (History of Magic, Care of Magical Creatures, Divination, Potions, and Muggle Studies to name a few) that, “[contain] no foolish wand-waving or silly incantations . . . .” However, that 10,080 hours also ignores any time learning/practicing spells out of class, and other extracurricular activities that would further hone a student’s reflexes (the Chamber of Secrets and Order of the Phoenix both mention a Dueling Club, and let’s not forget Quidditch). Also the books mention underaged magic in wizarding households is policed by the parents, allowing for more practice. I feel that 10,080 hours by the end of year seven is an educated guess for how many hours of practice your average wizarding student will have.
Let's assume it takes .75 seconds to cast a jinx/curse/hex. I feel like that’s a little bit longer than what they do in the movies, but let’s lowball for safety. How fast can a trained individual recognize an image?
Quite fast is the answer. MIT Researcher Mary Potter (and yes that is the real name of the researcher) says that the eye can recognize images in as little as 13 milliseconds (0.013 seconds). Given the amount of practice/training the students have received this seems reasonable.
http://news.mit.edu/2014/in-the-blink-of-an-eye-0116
So with 0.013 seconds to recognize the spell and 0.75 seconds to cast the appropriate defense, wizards would have 0.763 seconds to react. That’s about 2/3 of our lower limit, and about half our upper limit from earlier. Lets plug it into our formula from earlier. 30 feet/(0.763 seconds) ≈ 39.3184796854522 feet/second.
Thats 26.8080543309901 miles/hour. World record speed for the 100m dash is 27.8 miles/hour. So if you can dodge Usain Bolt running at you full tilt, you can dodge a spell.
But wait, there are trained professionals who dodge things faster than that all the time. Rodeo Aclowns. The top speed for some breeds of rodeo bulls is 35 miles/hour. Rodeo clowns have the enviable job description of “Lure the angry bull way from the bull rider. Don’t get trampled. Or gored.” And that’s just Monday.
If speed range varies, ranges for the speeds of spells could be 12.45–15.56 miles/hour, 20.45-25.56 miles/hour, or 26.81-35 miles/hour. My guess would be 12.45 being the speed of Hogwarts third years and those who don’t duel. 20.45-26.81 being the range of athletic seventh year students, and the 35 range being the location of Magical Law Enforcement's professionally trained hit wizards.
