why do we use 1.73?

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justin

Senior Member
i was asked earlier tonight why do we use the square root of three on 3 ph calcs and was unable to come up with a clear and understandable explanation. if anyone could help and maybe even post some great diagrams if needed that would be awesome! justin
 

Ed MacLaren

Senior Member
Re: why do we use 1.73?

Well, I should go to bed, but I'll get it started anyway. This usually takes an hour in the classroom with a digital projector, etc, etc.

It depends on where you are in math with regard to vectors, etc.

First of all, in a three phase system, the three voltages are "out of phase" with each other by 1/3 of a cycle or 120 degrees.

3ph1.gif


So you see that in a wye connection -
a. line voltage (E-line) = phase voltage (E-phase) x 1.732
b. line current (I-line) = phase current (I-phase)

In a delta connection, it is the opposite -
a. line voltage (E-line) = phase voltage (E-phase)
b. line current (I-line) = phase current (I-phase)x 1.732

The next thing to tackle is the power formula. To keep things simple, let's assume the load is non-inductive, with 100% power factor.

Single phase power - W (watts) = E (volts) x I (amps)

For three phase power, the formula used depends on whether you use the phase volt and amp values or the line volt and amp values.

Using phase values - W = E-phase x I-phase x 3

Using line values - W = E-line x I-line x 1.732

Make any sense so far?

Ed

[ September 19, 2003, 07:26 AM: Message edited by: Ed MacLaren ]
 

al hildenbrand

Senior Member
Location
Minnesota
Occupation
Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: why do we use 1.73?

The next level up in math invokes a small bit of trigonometry.

The tangent of the phase angle of 120? is exactly the square root of 3.

The tangent is the ratio of the length of the "opposite" side of the triangle from the angle in consideration, to the "adjacent" side. Looking at Ed's lower diagram, the opposite side is longest side between B & C, 208 Ft.
 
G

Guest

Guest
Re: why do we use 1.73?

Pound a stake in the ground. Call it stake #1. Walk 120-feet due south and pound in another stake. Call it stake # 2. Turn 90-degrees to the right and walk another 120-feet and pound in another stake. Call that stake #3. Walk another 120-feet due north. You don't have to pound another stake because you are back at stake #1.

QUESTION: Where is stake #1?

[Note to the oldtimers: I know it's an old riddle and I take no credit for it].

[ September 22, 2003, 02:03 AM: Message edited by: awwt ]
 

drg

Senior Member
Re: why do we use 1.73?

Following instructions it seems like a big "U" would have been made and stake #1 would be 120' away from where I am standing with stake #3.
 
G

Guest

Guest
Re: why do we use 1.73?

...ding, ding, ding...

We have a winner!

Answer: The North Pole.

Thanks for playing!
 

justin

Senior Member
Re: why do we use 1.73?

you're at your cabin and you step out the door and walk due south 300 yards, turn east and walk 300 yards and shoot a bear. you then walk due north 300 yards back to your cabin. what color is the bear? just a little flavor!!
 

charlie b

Moderator
Staff member
Location
Lockport, IL
Occupation
Retired Electrical Engineer
Re: why do we use 1.73?

The house in which you live has four walls, each with a southern view. A bear walks by your front window. What color is the bear?

Variations on an oldy-but-moldy puzzle. If I really had in interest, I might do some research to find out if there really are bears that live in that area of the planet.
 

bennie

Esteemed Member
Re: why do we use 1.73?

I don't think there is any life, other than ocean beings, at the geographic North Pole. The North Pole is ice over water, the South Pole is ice over a continent. I know there is no life except transient humans, at the South Pole.

I stood at the calculated exact center of the South Pole spin axis. All time and date lines mesh together at the pole. I effectively walked around the earth by walking in a small circle. This is a required initiation activity.

Standing at the pole, all directions are North.
 

wocolt

Member
Location
Ohio
Re: why do we use 1.73?

Tangent 90 is infin.: 91(degrees) would be -57.28 ad inf., and tan 120 is -1.73 or (Sq. root of 3??).
But 180 - 120 = 60 or 1.73.

WOC
 

wocolt

Member
Location
Ohio
Re: why do we use 1.73?

Just a further thought on the tangent.
Since Sin/Cos = Tan , and Sin90/Cos90 = 1/0
or infinity, then Sin91/Cos91 = .99984/-1.7E-2 =-57.2 and sin(120)/cos(120) = .866/-.5 = -1.73, since you cannot take the square root of a negative numnber this cant be .
The Cosine of this angle is in the second quadrant therefore is negative.
And as far as the power triangle goes:
S(apparent power) = VI
P(real power) = VI(Cos(theta)) or VI x Sq.Root(1-sin(Squared)(Theta)
Q(reactive power) = VI(Sin(theta)) or VI x Sq.Root(1-cos(Squared)(theta).
And finally the power factor PF = Cos(theta) or the ratio of P/S or as someone said Kw/Kva.


Aint math fun
WOC
 

al hildenbrand

Senior Member
Location
Minnesota
Occupation
Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: why do we use 1.73?

How do I measure this against the length of my body?
 

al hildenbrand

Senior Member
Location
Minnesota
Occupation
Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: why do we use 1.73?

No trick. You speak fluent math. For someone trying to equate voltage, current and power measurements at a 3? panel with a relationship to the basic calculations, the square root of 3 is a magic number. Some how each of us has to get "ahold" of where this constant comes from. How can this number be made palpable, concrete, touchable?
 

wocolt

Member
Location
Ohio
Re: why do we use 1.73?

Thank you for elaborating, Al, I must have over-reacted, all I saw was the 120 degrees. sorry , my bad.
But I see so many apprentices and journeymen alike taking short-cuts and not understanding why they are even possible.
Math is so important especially in our field, if you mention the phrase "Trig-Identity" all you get a blank stare, maybe its me, but I think these things should be taught. There seems to be this stigma with mathematics that its just too much trouble, my God, it is not like were are asking them to do 'Dot and Cross' products.

WmColt
 
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