Solar Panel Tilt Bracket Ideal Azimuth Formula Strike Angle

[albert436]

Always appreciate another perspective.

We all have things that appeal to our interest. My background in geometry/math/etc isn't as much as these other fellows, and in CAD/computers/3D modelling not as much as yours.

Just trying to learn something here.

I know there has been a lot of back and forth on this thread so this may have been overlooked in the shuffle:

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Purely a mental exercise just to stretch the brain.

So let's not throw out the baby with the bathwater ! ! !

Oh dear god. I hope you guys are having fun. I do hope that no one stumbles onto this and thinks there is anything of substance here that would help optimize an array's orientation. The geometric manipulations and ray tracing are all interesting ways to go about it, but really, the easiest way to estimate solar access is to get a Suneye/Pathfinder/etc up on the roof and make measurements in the orientations being considered. A good solar installer will do that as part of their site survey. Shading from the roof, or trees, or other obstructions will be accounted for, and the best orientation can be found without much more work. For the most part, anyone pushing an array at something other than flush mount is probably trying to squeeze some extra profit out... smart money will just stick with flush mount and add a couple panels as needed, unless space is really too tight.

I use 3D modelling software to figure out the equivalent Azimuth/Tilt plane for Poa irradiance calculations created when a panel is oriented with azimuth, tilt, and "sideways tilt", as you called it. More specialized software (incorporating the solar path) is necessary to determine how to lay out the panels to avoid external and self-shading in the compound orientation.

NREL's SAM (System Advisor Model) has a 3d shade modelling engine... it is free, but takes some time to learn.

[J.P.M.]

Oh dear god. I hope you guys are having fun. I do hope that no one stumbles onto this and thinks there is anything of substance here that would help optimize an array's orientation. The geometric manipulations and ray tracing are all interesting ways to go about it, but really, the easiest way to estimate solar access is to get a Suneye/Pathfinder/etc up on the roof and make measurements in the orientations being considered. A good solar installer will do that as part of their site survey. Shading from the roof, or trees, or other obstructions will be accounted for, and the best orientation can be found without much more work. For the most part, anyone pushing an array at something other than flush mount is probably trying to squeeze some extra profit out... smart money will just stick with flush mount and add a couple panels as needed, unless space is really too tight.

Thank you for the sanity check. I'm outa' this cluster function.

[sensij]

Oh dear god. I hope you guys are having fun. I do hope that no one stumbles onto this and thinks there is anything of substance here that would help optimize an array's orientation. The geometric manipulations and ray tracing are all interesting ways to go about it, but really, the easiest way to estimate solar access is to get a Suneye/Pathfinder/etc up on the roof and make measurements in the orientations being considered. A good solar installer will do that as part of their site survey. Shading from the roof, or trees, or other obstructions will be accounted for, and the best orientation can be found without much more work. For the most part, anyone pushing an array at something other than flush mount is probably trying to squeeze some extra profit out... smart money will just stick with flush mount and add a couple panels as needed, unless space is really too tight.

[posplayr]

I can see that, I think, but what I mean is that the lower panels on the roof, if they were on a roof that was truly oriented to the SE with no shading whatsoever, they'd still get sun until the sun was perpendicular to them, approximately.

But I am trying to visualize whether, when the roof is actually oriented toward the NE, if the lower down panels on the roof would have their sun cut off by the top part of the roof.

I'm imagining an array where the bottom edge of the panels is touching the surface of the roof.

The more I think about it -- the lower the sun is to the horizon, and the further back (to the north) on the roof the panel is, might the effect be more, as the sun goes past the edge of that NE facing roof? Despite the fact that the panel is facing a more favorable direction.

Did I miss the point or not explain it well the first time ?

Yes a model would help, going out of town for ten days later this week and a bit busy so it might need to wait.

This is an interesting discussion. I do have some 3x5 cards I can use to represent panels, probably need a carboard box or something to represent the roof. Figuring out the path of the sun, that is another little aspect to work out. But as I say, interesting.

You are not being very clear, so I hate to comment. Most of the answers to your questions are going to come from simple ray tracing.
Realize two thing that involve any calculation of optimal plane orientation.

1.) The amount of solar irradiance available (energy available from the sun) goes down as the cos of the angle from the vertical in two directions. You can think of it as the lower the angle the lower the density of the parallel light beams that are distributed across a larger area on the ground.

2.) The amount of that available solar irradiance captured is also a function of cos(angle) of the panel to this incident angle.

So for an optimally oriented panel for just solar collection, you tend to have a cos(theta) ^2 effect. 45 degrees off from vertical and 45 degrees off from pointing is 1/2 power harvested taking both factors into effect. So (to state the obvious) most of the power you are going to collect is going to be when the sun is high and the panels are looking right into the sun. Well the less obvious factor is that at low sun angles at wide angular mismatch to the panel there is very little energy available so missing (due to shading) is really not much of a penalty. If shading is bad then there are the micro inverter solutions that can optimize better than string inverters.

All of these factors are incorporated into a typical model like PVWatts and the website listed also took most of this into account in the calculation on the "best compromise" for energy collection (otherwise known as optimal). I suspect beyond about 45 degrees there is a diminishing return and so shading that might occur at 30 degrees above the horizon is not affecting production to any significant amount.

Without a tracker you're just giving up a lot of energy no matter how you slice it.

[albert436]

I can see that, I think, but what I mean is that the lower panels on the roof, if they were on a roof that was truly oriented to the SE with no shading whatsoever, they'd still get sun until the sun was perpendicular to them, approximately.

But I am trying to visualize whether, when the roof is actually oriented toward the NE, if the lower down panels on the roof would have their sun cut off by the top part of the roof.

I'm imagining an array where the bottom edge of the panels is touching the surface of the roof.

The more I think about it -- the lower the sun is to the horizon, and the further back (to the north) on the roof the panel is, might the effect be more, as the sun goes past the edge of that NE facing roof? Despite the fact that the panel is facing a more favorable direction.

Did I miss the point or not explain it well the first time ?

Yes a model would help, going out of town for ten days later this week and a bit busy so it might need to wait.

This is an interesting discussion. I do have some 3x5 cards I can use to represent panels, probably need a carboard box or something to represent the roof. Figuring out the path of the sun, that is another little aspect to work out. But as I say, interesting.

[posplayr]

Two things that aren't clear to me.

How does one figure out how far apart the rows need to be staggered ? Does the rotation in that plane affect that? I mean the fact that the panels are "tilted" (I would think not but on the other hand, maybe so . . . ) How hard is it to figure out ?

Draw yourself a picture. For any two panels that are out of plane (i.e. "staggered"), one will shade the other as some point in the day. The question then is how much will it shade or equivalently how low of a sun angle to I want to to provide sufficient space so that no shading occurs.
If you know a little trigonometry you can figure it out. As a starting point use 45 degree sun angle, then the space between head and toe of adjoining staggered panels is equal to the vertical offset between the head and the toe of the shading panel. If the sun angle for no shading is reduced further then the spacing increases as Spacing =Height / tan(sun angle - rad). Obviously the more you have to rotate to find a new roof alignment, the larger Height gets as it goes from opposite corners (which now stand higher) the larger the spacing needs to be.

One way of doing this without using a 3D CAD program is to build a small model. With a light source you can get a pretty good idea of what sun angles will do and where the shading will occur.

The other thing -- let's say the roof is oriented toward NE. If we tilt the panels to orient toward SE, then at some point in the afternoon won't the peak of the roof start cutting off the sunlight? And how does one figure that out ? I recognize that the sun's path varies through the year but we don't let that bother us too much normally when deciding upon any particular fixed panel array, do we ? We look for an optimal solution, right ?

Thanks!

I think you might be getting confused. The optimal geographical angel is the one that harvests the most sun or maximizes some economic criteria. That is what the computer simulations are for. Here is a link to give you "optimal " solutions according to the criteria the author used to maximize his objectives. The answer is some fixed angle generally just a fixed angle with respect to true south. If there is a time of day rate element added to develop a maximum $ harvest there is probably a azimuth offset also involved. It is still just a fixed angle even if described by two parameters. It is optimal if you believe the authors calculations or you can use PV watts to see if it also works out for you.

http://www.solarpaneltilt.com/

So when you talk about changing tilt you are immediately diverging from the fixed optimal direction(i.e. the model output). All bets are off unless you can find a model that allows to to change it but presumably you will only lower the metrics being optimized.

However if you simply rotate about the optimum angle (the normal), you will not have violated anything and you are free to find something that you can mount as those new orientations for better esthetics.

The other way to look at this is , if the optimal solution is given in terms of N/S tilt, what will it take for you to built a synthetic plane at that angle above your roof that is not mounted in line with N-S. Same problem.

It should become more obvious as you go down this path that the further the house is off of N-S the more compromise or the more complexity you will have in trying to achieve it. At that point the only way to figure it is a detailed cost break down of the detailed install.

[albert436]

Two things that aren't clear to me.

How does one figure out how far apart the rows need to be staggered ? Does the rotation in that plane affect that? I mean the fact that the panels are "tilted" (I would think not but on the other hand, maybe so . . . ) How hard is it to figure out ?

The other thing -- let's say the roof is oriented toward NE. If we tilt the panels to orient toward SE, then at some point in the afternoon won't the peak of the roof start cutting off the sunlight? And how does one figure that out ? I recognize that the sun's path varies through the year but we don't let that bother us too much normally when deciding upon any particular fixed panel array, do we ? We look for an optimal solution, right ?

Thanks!

[posplayr]

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

JPM,
I have left you an open invitation to “take your best shot”. We can now see (for you) what that amounts to:
• Vague notions of engineering and unsubstantiated personal opinions on technical subjects
• Generous display of your solar laurels
• References to people you know high solar places
• And unsolicited personal opinions which are little more than personal attacks.

When I pointed out your lack of comprehension of the discussion, you still failed to make even one cogent technical point that might have demonstrated some minimal level of understanding. It is apparently completely over your head. To remind you this was the subject:

I attached a picture of what I am planning to do. The calculations can't be done with typical software. I will need to come up with a formula.

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Anyone have any ideas?

I might have asked about this on another thread, I think I referred to it as a "sideways tilt".

My answer to these inquiries was concise, elegant, geometrical, and to the point.

Any fixed panel tilt angle from one set of coordinates can be transformed into another frame using Euler Angles. More importantly any optimality that the original panel orientation might have (pick your metrics or program) can be transformed to a new roof line orientation by a simple rotation about the panel normal and without loss of optimality.

In a simple example to demonstrate the principle, consider a shallow hip roof not aligned with North South, but rather in between cardinal directions. Further assume that the optimal panel has a shallow tilt angle typically higher than the roof pitch (it is easier to visualize). You can easily transform the optimal fixed mounting orientation of the panel (assuming N-S) to another set of directions by simply rotating the panel about the (close to vertical) normal until the horizontal projection of the panel is in line with any alternate roof line. While , this can be all calculated using direction cosines, I did not have to add that level of detail. The principle can be visualized and implemented by purely geometrical methods.

• You complained that direction cosines are too complex; only for someone that is not degreed and I’m starting to see that that seems to fit you.
• You complained that Euler angles do not take into account the great variety of solar considerations; you failed to recognize the fundamental fact that the problems of optimal positions and translation to other roof lines are analytically separable processes. It is a two-step solution that will accommodate any set of constraints or objectives because the second part, the translation to different roof lines, only need to know the optimal fixed panel orientation.
• You complained I made it too complex; you are the one that has over complicated the discussion and failed to see the simplifying principles that maintain optimality.
• You are the one that does not seem to understand any of what was posted; Even albert436 seems to get it.

I totally get this.

You complain that I am a danger to the forum for spreading unsound advice; It is clear that you are the one without technical acumen and often exhibit a total failure to understand basic engineering. The key to understanding this fact is in the decisions you reach.

You have an overt tendency is to offer personal opinions and personal attacks much more than any technical concept. I guess It is all part of the package for someone so insecure that they must pontificate on topics that clearly go beyond their grasp, and attempt to demean other just to elevate themselves.

The offer is still open “take your best shot”, anything technical. Based on past performance, I’m not holding my breath.

[posplayr]

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

JPM,
I have left you an open invitation to “take your best shot”. We can now see (for you) what that amounts to:
• Vague notions of engineering and unsubstantiated personal opinions on technical subjects
• Generous display of your solar laurels
• References to people you know high solar places
• And unsolicited personal opinions which are little more than personal attacks.

When I pointed out your lack of comprehension of the discussion, you still failed to make even one cogent technical point that might have demonstrated some minimal level of understanding. It is apparently completely over your head. To remind you this was the subject:

I attached a picture of what I am planning to do. The calculations can't be done with typical software. I will need to come up with a formula.

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Anyone have any ideas?

I might have asked about this on another thread, I think I referred to it as a "sideways tilt".

My answer to these inquiries was concise, elegant, geometrical, and to the point.

Any fixed panel tilt angle from one set of coordinates can be transformed into another frame using Euler Angles. More importantly any optimality that the original panel orientation might have (pick your metrics or program) can be transformed to a new roof line orientation by a simple rotation about the panel normal and without loss of optimality.

In a simple example to demonstrate the principle, consider a shallow hip roof not aligned with North South, but rather in between cardinal directions. Further assume that the optimal panel has a shallow tilt angle typically higher than the roof pitch (it is easier to visualize). You can easily transform the optimal fixed mounting orientation of the panel (assuming N-S) to another set of directions by simply rotating the panel about the (close to vertical) normal until the horizontal projection of the panel is in line with the selected roof line. While , this can be all calculated using direction cosines, I did not have to add that level of detail. The principle can be visualized and implemented by purely geometrical methods.

• You complained that direction cosines are too complex; only for someone that is not degreed and I’m starting to see that that seems to fit you.
• You complained that Euler angles do not take into account the great variety of solar considerations; you failed to recognize the fundamental fact that the problems of optimal positions and translation to other roof lines are analytically separable processes. It is a two-step solution that will accommodate any set of constraints or objectives because the second part, the translation to different roof lines, only need to know the optimal fixed panel orientation.
• You complained I made it too complex; you are the one that has over complicated the discussion and failed to see the simplifying principles that maintain optimality.
• You are the one that does not seem to understand any of what was posted; Even albert436 seems to get it.

I totally get this.

You complain that I am a danger to the forum for spreading unsound advice; It is clear that you are the one without technical acumen and often exhibit a total failure to understand basic engineering. The key to understanding this fact is in the decisions you reach.

You have an overt tendency is to offer personal opinions and personal attacks much more than any technical concept. I guess It is all part of the package for someone so insecure that they must pontificate on topics that clearly go beyond their grasp, and attempt to demean other just to elevate themselves.

The offer is still open “take your best shot”, anything technical. Based on past performance, I’m not holding my breath.

[posplayr]

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

JPM,
I have left you an open invitation to “take your best shot”. We can now see (for you) what that amounts to:
• Vague notions of engineering and unsubstantiated personal opinions on technical subjects
• Generous display of your solar laurels
• References to people you know high solar places
• And unsolicited personal opinions which are little more than personal attacks.

When I pointed out your lack of comprehension of the discussion, you still failed to make even one cogent technical point that might have demonstrated some minimal level of understanding. It is apparently completely over your head. To remind you this was the subject:

I attached a picture of what I am planning to do. The calculations can't be done with typical software. I will need to come up with a formula.

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Anyone have any ideas?

I might have asked about this on another thread, I think I referred to it as a "sideways tilt".

My answer to these inquiries was concise, elegant, geometrical, and to the point.

Any fixed panel tilt angle from one set of coordinates can be transformed into another frame using Euler Angles. More importantly any optimality that the original panel orientation might have (pick your metrics or program) can be transformed to a new roof line orientation by a simple rotation about the panel normal and without loss of optimality.

In a simple example to demonstrate the principle, consider a shallow hip roof not aligned with North South, but rather in between cardinal directions. Assume further that the panel has a shallow tilt angle typically higher than the roof pitch (it is easier to visualize). You can easily transform the optimal fixed mounting orientation of the panel (assuming N-S) to another set of directions by simply rotating the panel about the (close to vertical) normal until the horizontal projection of the panel is in line with the selected roof line. While , this can be all calculated using direction cosines, I did not have to add that level of detail. The principle can be visualized and implemented by purely geometrical methods.

• You complained that direction cosines are too complex; only for someone that is not degreed and I’m starting to see that that seems to fit you.
• You complained that Euler angles do not take into account the great variety of solar considerations; you failed to recognize the fundamental fact that the problems of optimal positions and translation to other roof lines are analytically separable processes. It is a two-step solution that will accommodate any set of constraints or objectives because the second part, the translation to different roof lines, only need to know the optimal fixed panel orientation.
• You complained I made it too complex; you are the one that has over complicated the discussion and failed to see the simplifying principles that maintain optimality.
• You are the one that does not seem to understand any of what was posted; Even albert436 seems to get it.

I totally get this.

You complain that I am a danger to the forum for spreading unsound advice; It is clear that you are the one without technical acumen and often exhibit a total failure to understand basic engineering. The key to understanding this fact is in the decisions you reach.

You have an overt tendency is to offer personal opinions and personal attacks much more than any technical concept. I guess It is all part of the package for someone so insecure that they must pontificate on topics that clearly go beyond their grasp, and attempt to demean other just to elevate themselves.

The offer is still open “take your best shot”, anything technical. Based on past performance, I’m not holding my breath.

[posplayr]

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

JPM,
I have left you an open invitation to “take your best shot”. We can now see (for you) what that amounts to:
• Vague notions of engineering and unsubstantiated personal opinions on technical subjects
• Generous display of your solar laurels
• References to people you know high solar places
• And unsolicited personal opinions which are little more than personal attacks.

When I pointed out your lack of comprehension of the discussion, you still failed to make even one cogent technical point that might have demonstrated some minimal level of understanding. It is apparently completely over your head. To remind you this was the subject:

I attached a picture of what I am planning to do. The calculations can't be done with typical software. I will need to come up with a formula.

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Anyone have any ideas?

I might have asked about this on another thread, I think I referred to it as a "sideways tilt".

My answer to these inquiries was concise, elegant, geometrical, and to the point.

Any fixed panel tilt angle from one set of coordinates can be transformed into another frame using Euler Angles. More importantly any optimality that the original panel orientation might have (pick your metrics or program) can be transformed to a new roof line orientation by a simple rotation about the panel normal.

In a simple example to demonstrate the principle, consider a shallow hip roof not aligned with North South, but rather in between cardinal directions. Assume further that the panel has a shallow tilt angle typically higher than the roof pitch (it is easier to visualize). You can easily transform the optimal fixed mounting orientation of the panel (assuming N-S) to another set of directions by simply rotating the panel about the (close to vertical) normal until the horizontal projection of the panel is in line with the selected roof line. While , this can be all calculated using direction cosines, I did not have to add that level of detail. The principle can be visualized and implemented by purely geometrical methods.

• You complained that direction cosines are too complex; only for someone that is not degreed and I’m starting to see that that seems to fit you.
• You complained that Euler angles do not take into account the great variety of solar considerations; you failed to recognize the fundamental fact that the problems of optimal positions and translation to other roof lines are analytically separable processes. It is a two-step solution that will accommodate any set of constraints or objectives because the second part, the translation to different roof lines, only need to know the optimal fixed panel orientation.
• You complained I made it too complex; you are the one that has over complicated the discussion and failed to see the simplifying principles that maintain optimality.
• You are the one that does not seem to understand any of what was posted; Even albert436 seems to get it.

I totally get this.

You complain that I am a danger to the forum for spreading unsound advice; It is clear that you are the one without technical acumen and often exhibit a total failure to understand basic engineering. The key to understanding this fact is in the decisions you reach.

You have an overt tendency is to offer personal opinions and personal attacks much more than any technical concept. I guess It is all part of the package for someone so insecure that they must pontificate on topics that clearly go beyond their grasp, and attempt to demean other just to elevate themselves.

The offer is still open “take your best shot”, anything technical. Based on past performance, I’m not holding my breath.

[posplayr]

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

JPM,
I have left you an open invitation to “take your best shot”. We can now see (for you) what that amounts to:
• Vague notions of engineering and unsubstantiated personal opinions on technical subjects
• Generous display of your solar laurels
• References to people you know high solar places
• And unsolicited personal opinions which are little more than personal attacks.

When I pointed out your lack of comprehension of the discussion, you still failed to make even one cogent technical point that might have demonstrated some minimal level of understanding. It is apparently completely over your head. To remind you this was the subject:

I attached a picture of what I am planning to do. The calculations can't be done with typical software. I will need to come up with a formula.

Reviving this thread just out of curiosity. The neighbors have cut down some trees so I don't need to worry about it.

But for the sake of academics--how do you figure these angles?

Anyone have any ideas?

I might have asked about this on another thread, I think I referred to it as a "sideways tilt".

My answer to these inquiries was concise, elegant, geometrical, and to the point.

Any fixed panel tilt angle from one set of coordinates can be transformed into another frame using Euler Angles. More importantly any optimality that the original panel orientation might have (pick your metrics or program) can be transformed to a new roof line orientation by a simple rotation about the panel normal.

In a simple example to demonstrate the principle, consider a shallow hip roof not aligned with North South, but rather in between cardinal directions. Assume further that the panel has a shallow tilt angle typically higher than the roof pitch (it is easier to visualize). You can easily transform the optimal fixed mounting orientation of the panel (assuming N-S) to another set of directions by simply rotating the panel about the (close to vertical) normal until the horizontal projection of the panel is in line with the selected roof line. While , this can be all calculated using direction cosines, I did not have to add that level of detail. The principle can be visualized and implemented by purely geometrical methods.

• You complained that direction cosines are too complex; only for someone that is not degreed and I’m starting to see that that seems to fit you.
• You complained that Euler angles do not take into account the great variety of solar considerations; you failed to recognize the fundamental fact that the problems of optimal positions and translation to other roof lines are analytically separable processes. It is a two-step solution that will accommodate any set of constraints or objectives because the second part, the translation to different roof lines, only need to know the optimal fixed panel orientation.
• You complained I made it too complex; you are the one that has over complicated the discussion and failed to see the simplifying principles that maintain optimality.
• You are the one that does not seem to understand any of what was posted; Even albert436 seems to get it.

I totally get this.

You complain that I am a danger to the forum for spreading unsound advice; It is clear that you are the one without technical acumen and often exhibit a total failure to understand basic engineering. The key to understanding this fact is in the decisions you reach.

You have an overt tendency is to offer personal opinions and personal attacks much more than any technical concept. I guess It is all part of the package for someone so insecure that they must pontificate on topics that clearly go beyond their grasp, and attempt to demean other just to elevate themselves.

The offer is still open “take your best shot”, anything technical. Based on past performance, I’m not holding my breath.

[J.P.M.]

JPM you clearly did not comprehend what I posted; I'll give you the benefit of the doubt you did not even read it.

Assume what you want. I believe I understand what you posted, and in addition, and also in my professional opinion, I believe I know more about what you wrote as it pertains to solar energy resource assessment, and for that matter to engineering in general and mechanical engineering in particular, than you do.

Your description of what's required is, IMO, cryptic, technically clumsy to use for the application being discussed, and shows your ignorance of available and long standing technology that I've known about, studied and helped advance over the last 40+years to the extent your embarrassing yourself to not only me, but also to other folks who know something of the subject. Your written demeanor reminds me of the type of communication I'd get from someone who's in a subject way over their head.

Furthermore, your descriptions are, IMO, incomplete in describing what's required to the point of being misleading. I suspect however, that's done out of ignorance. Even so, that's unprofessional. Similar to the last dust up we (you and I) had over thermal time constants where you showed off your ignorance of heat transfer in particularly stunning ways, I'm of the opinion and suspicion you're in over your head on these currently being discussed aspects of solar technology and of engineering in general as it pertains to solar energy. Looks to me like the latest example of a little knowledge being a dangerous thing.

FWIW, I usually refrain from comments on subjects I'm ignorant about in the hope I'll not lead someone astray and embarrass myself in the process.

To the extent you continue making statements that are incorrect and misleading, and as a result perhaps causing readers to reach incorrect conclusions and act on them, I will comment on such statements.

Other than that, I have no intention of getting into an infantile like pissing match of the type this forum recently experienced as it's a waste of my time, hampers communication, and is harmful to the subject that's the sign over the door, which subject caused me to change careers and take up engineering as a profession about 40 or so years ago.

As the probable aggrieved party in this exchange, I'll leave the last word/comment to you.

[posplayr]

2.) On Posplayr's comments: Standard geometrical methods are the basis, in a strictly mathematical sense, for calculations dealing with a vector's orientation relative to a surface, or between two, or several vectors or between two surfaces, or other purposes.

For solar work, the position of the sun, and hence the angle of incidence (the direction) of the beam portion of the solar irradiance relative to a surface of arbitrary orientation, requires a form those calculations. But when used in the form suggested, Euler #'s or direction cosines or other methods are cumbersome, and in any case are not sufficient to get you what you need. No offense, but the tax credits will probably expire before you will be familiar enough in the use of such things, and you still won't have what you're looking for, because more is needed. That's the wrong way to go about it. Folks I know who are knowledgeable about such things and also about solar positioning use methods suited for the purpose at hand. Those methods are readily available. See Duffie & Beckman, chap. 1.

.

JPM you clearly did not comprehend what I posted; I'll give you the benefit of the doubt you did not even read it.

[J.P.M.]

Albert: Sounds like the shading is no longer an issue. With that assumption:

1.) It seems what you are looking for, at least at this time, is en estimate of what the annual production enhancement might be between a panel orientation which is the same as the roof, and some other orientation(s) using some mounting/tilting scheme(s) that utilizes slightly different racking and mounting methods made for that purpose.

2.) On Posplayr's comments: Standard geometrical methods are the basis, in a strictly mathematical sense, for calculations dealing with a vector's orientation relative to a surface, or between two, or several vectors or between two surfaces, or other purposes.

For solar work, the position of the sun, and hence the angle of incidence (the direction) of the beam portion of the solar irradiance relative to a surface of arbitrary orientation, requires a form those calculations. But when used in the form suggested, Euler #'s or direction cosines or other methods are cumbersome, and in any case are not sufficient to get you what you need. No offense, but the tax credits will probably expire before you will be familiar enough in the use of such things, and you still won't have what you're looking for, because more is needed. That's the wrong way to go about it. Folks I know who are knowledgeable about such things and also about solar positioning use methods suited for the purpose at hand. Those methods are readily available. See Duffie & Beckman, chap. 1.

3.) Try this:

- Get a decent estimate of the orientation of the surface your proposed array will be mounted on. This means get the surface azimuth and the surface tilt. The accuracy is not SUPER critical, but as close as possible is best. GIGO. Google earth and a protractor on a computer screen will work to get an azimuth. A compass will also work, but don't forget to correct for magnetic declination. For elevation angle, projecting the roof slope to the ground and using a protractor set along that imaginary line is not a terrible 1st approx. for a tilt (elevation) angle.

- Find PVWatts on the net. READ THE HELP/INFO SCREENS. Try a few runs go get familiar with how it works and some of the flexibility/limits of model. If you are more than 10 miles from thje coast use Miramar #'s. if close to the coast use Lindbergh or Carlsberg. Remember the results are long term estimates of output, not predictions, and certainly not for short term guesses.

After you get your feet wet, for your starting orientation, use the roof azimuth and elevation angles you've measured. Also, set the system losses # at about 10%. Long story on that. For now, I suggest just set it at 10%. Consider that your "base case". Set the system size for now at 1kW. For a 1st SWAG, set the electricity cost at $0.25/kWh.

- Get the monthly output and "energy value" (savings) savings and save the results somewhere.

- Next, rerun PVWatts, this time changing the orientation ( the surface azimuth and tilt) to what you might think is a possible or wanted orientation using tilted racking or other means to change the position (orientation) of the panels.

- Get the monthly output and savings for that new orientation and save the results in the same place you saved the first set of results.

- Compare the two. Dividing one output by the other will give you a % enhancement. Subtract one energy value from the other for savings or additional cost.

- As a 1st approx., choose any system size (in kW) and multiply that system size (in kW) by the PVWatts output for an estimate of that system size output and savings.

4.) If you are considering a "sawtooth" or staggered row arrangement, PVWatts won't give reasonable results. Reason: PVWatts does not account for shading and rows of panels will shade the rows of panels to the north, often called self shading.

For self shading you'll need other software. SAM, which is sort of like PVWatts on steroids will do a fair job. However, without some fair amount of background on the subject of solar energy, that can cause confusion and lead to erroneous conclusions.

I encourage learning, but for right now, it seems you may have more immediate and pressing concerns.

5.) As a practical matter around here (San Diego), the additional distance between rows required to avoid self shading by rows in front (to the south in our case) that is required usually makes sawtooth or staggered row arrangements impractical and not as good a performer as you might think. Even if there is some improvement in annual production, the extra cost in engineering, materials and labor is usually not worth it when compared to the relatively small increase in electricity cost savings.

Take what you want of the above. Scrap the rest.