Wind Turbine Tip Speed Ratio

The Tip Speed Ratio (TSR) is used by current of air turbine designers to properly match and optimize a blade set to a particular generator (i.e. the permanent magnet alternator). This is important to respond one of the well-nigh mutual questions we go: What size blades should I choose to match with my generator?

We endeavour to help you answer this question past focusing on explaining the simple physics behind computing the Tip Speed Ratio!

Understanding Tip Speed Ratio

Past definition, TSR is the speed of the blade at its tip divided past the speed of the wind. For instance, if the tip of a blade is traveling at 100 mph (161 kph) and the wind speed is 20 mph (32 kph or nine yard/s), then the TSR is 5 (100 mph/20 mph). Simply put, the tip of the blade is traveling five times faster than the speed of the current of air.

At present, you must exist wondering why this is important. For a particular generator, if the blade set spins also slowly then about of the wind volition pass by the rotor without being captured by the blades. If the blades spin too fast, and so the blades volition ever be traveling through used/turbulent wind. This is because the blades will ever be traveling through a location that the blade in front of it just traveled through (and used up all the wind at that place). Information technology is important that enough time lapses between two blades traveling through the aforementioned location so that new/unused current of air tin enter this location. Thus, the side by side bract that passes through this location volition be able to harness fresh/unused wind. In short, if the blades are likewise ho-hum they are not capturing all the wind they could and if they are too fast, so the blades are spinning through used/turbulent air current. For this reason, TSR's are employed when designing air current turbines and so that the maximum amount of energy can be extracted from the wind using a particular generator.

Without going into details, physics and research have shown that the approximate optimal TSR'south for a given blade rotor are:

TSR	Number of Blades
~vi-7	ii
~5-6	3
~2-3	v

There are many of import conclusions one can describe from analyzing TSR's. For the do-information technology-yourselfer that is putting together their ain air current generator, let'southward go over a few of the well-nigh basic and important points:

Rotors with many blades (i.e. 11 blades) are mostly not a skilful idea. An 11 bladed rotor would take an optimal TSR which is very low. This ways an 11 bladed rotor would operate nigh efficiently at extremely depression rpm's. Because nearly all generators (permanent magnet alternators) are non optimized for extremely low rpm's, there is no reward or reason to use a rotor with many blades. Remember, rotors with lots of blades are capturing used/turbulent wind at high TSR's and are thus extremely inefficient if used as a high-rpm blade set. This is a very important point considering many people intuitively think that more blades equal a faster and more than efficient blade prepare. But, the laws of physics say that this is not true.
If you already have a generator or a motor and it requires high rpm's to reach charging voltage, then your all-time bet is a 2 or iii blade rotor. These rotors operate more efficiently at high rpm'south. Likewise, keep the blades as short as pragmatically possible because shorter blades obviously spin faster than longer blades.
Last but not least, keep in mind the Tip to Speed Ratio! If your wind generator rotor is operating at a low TSR compared to the optimum value, and then your wind turbine's blades will tend stall earlier hitting maximum ability/efficiency. If the wind turbine's blades are spinning above the recommend TSR, and so the blades will exist traveling through turbulent wind. Non only is this inefficient, the turbulent wind puts your blades and entire wind turbine nether unnecessary stress and fatigue.

How to Measure TSR

Measuring the TSR of a blade ready is fairly easy. To achieve this measurement you lot volition need 2 things:

A digital tachometer. These are bachelor online for almost 25 USD and tin can be used to measure out the rpm's of a blade set.
A anemometer. A digital anemometer can exist purchased online for fairly cheap (~twenty USD) and is used to measure the wind speed.

With these two items, you lot can obtain the necessary measurements to summate TSR's. But, ane question does remain. How do we calculate the speed at the tip of a wind turbine blade, if we only know the rpm at the tip of the blade from our tachometer measurement? Well, we have to practice a fiddling math. Let's suspension down this calculation footstep by footstep:

Distance the tip of the bract travels to complete 1 revolution = circumference of a circle with radius r = (two)(?)(r)
where r = the length of the bract.

Sample Calculation

What distance does a one meter bract travel to complete one revolution?
Answer: Distance = (ii)(?)(r) = (2)(?)(1 meter) = 6.28 meters

Now, let'southward assume nosotros measure an rpm of 450 at the tip of the blade using our digital tachometer. How far does the tip of the blade travel in one hr?

Reply: 450 rpm = 450 (rotations)/(minute) = 450 r/min
(450 r/min) 10 (60 min/hour) = 27000 rotations per 60 minutes = 27000 r/hour

(27000 r/hour) 10 (1 hour) = 27000 rotations

(27000 rotations) x (6.28 meters/rotation) = 169,560 meters
Note: we know that the blade tip travels half-dozen.28 meters in 1 rotation because this is the starting time calculation we did!
And then, at present we know that the tip of the blade travels 169,560 meters in one hour. Now, let's catechumen the meters to miles:
169,560 meters x (1 mile)/(1609 meters) = 105 miles

Alright, we are near finished. At present nosotros have to summate the speed at the tip of the blade. This is easy considering we know the tip of the blade traveled 105 miles in one hour. Run across calculation below:
Distance = (charge per unit) 10 (time) and rate = (distance)/(time)

Rate = (105 miles)/(1 60 minutes) = 105 miles/60 minutes = 105 mph

That's it! The tip speed of this particular blade is 105 mph at 450 rpm. So what if the current of air was bravado at 20 mph when we measured 450 rpm. What is the TSR? That'south easy:

TSR = (Bract tip speed)/(air current speed) = (105 mph)/(xx mph) = 5.3