CPESR Surveying Course Review

This review is about the online course I took in studying for the April 2017 California Engineering Surveying Exam. Having never taken a surveying course in college and learning most of it on the job, I needed instruction so that I could understand the basics. There are many courses that can teach you surveying from scratch, but I decided to go with the on-demand Civil PE Surveying Review (CPESR) course taught by Kirk Torossian based on reviews from engineerboards.com

Of all the courses I could find that have an online option, CPESR was the cheapest at $350. The course includes 12 hours of on-demand videos, practice quizzes, four timed computer-based test (CBT) exams, a reference manual with equations and example problems, and a cool transparent ruler.

Reference Manual
Your references are one of the most important things you need on the exam besides your calculator, and I feel that the reference manual that comes with course is helpful for 90% of the questions encountered on this exam. The manual comes pre-tabbed with the important topics and relevant formulas. Relevant sections from the various surveying acts and laws are included and easy to find. All of the class video sample exercises are within the manual as well.


This manual is great for answering the many quantitative questions in the exam, but since it’s not a standalone book you won’t be able to find the answer to any specific “trivial” questions the exam sometimes throws at you. Because of this, I highly recommend purchasing an additional reference that covers every topic more in-depth, or perhaps a textbook. My personal suggestion is to purchase or borrow a copy of Dr. Mansour’s “Surveying for California Civil PE License” or Reza Mahallati’s “Civil Surveying Review Workbook” ($130 on his website). Each of these workbooks are part of each instructor’s respective course, so you should also consider weighing the CPESR course against these competitor courses as well.

Video Content & Online Interface
There are only 12 hours of on-demand video in this class. This doesn’t seem like a lot for the price you’re paying, but CPESR makes up for it by being concise and offering the best quality and presentation of any on-demand course I took while studying for the three PE exams. The videos are split into roughly nine sections of surveying topics, and they range from 30 minutes to two hours long.

The online interface is also easy to navigate and you can access the website and videos on most tablets as well (a bonus if you want to study in bed or on the bus).

The Teacher
Kirk’s teaching style is upbeat and kept me engaged. I’ve taken online courses that seem to drag on because of the seriousness of the instructor or a monotone voice, but this class isn’t like that. Kirk speaks very clearly and throws in some humor to keep things light. In the videos he’ll go over a topic, and then show you how to solve example questions directly from the reference manual.

Speed is emphasized in this class, and the really nice thing about the videos is that at times he shows the exact buttons to press on the calculator (a TI-89, which he recommends, but more on that later) so that you can maximize your speed, and he explains each step of the problem thoroughly and shows you a slow and fast way to solve a problem.

Overall, Kirk teaches and speaks to you more like he’s your gym buddy rather than a formal instructor, and this makes watching the videos and learning a relatively dry topic (sorry, but I’m a water resources dude) more enjoyable.

Computer Based Quizzes
After viewing the videos for each section, you are encouraged to take a quiz that tests you on basic questions about that topic and that builds on the previous topics. This is a nice feature that I appreciated because it kept everything fresh in my mind up to the end of the course. Also, the quizzes are setup exactly like the CBTs with four multiple choice answers to simulate the real test.

Computer Based Tests (CBTs)
There are four, 55-question, 2.5-hour long, randomized CBTs in this class, and they range from easy, to normal, to hard, to very hard. You can take these tests over and over, and each time you complete a test you receive the solutions, and your score is saved so you can gauge your performance over time.

Kirk’s advice is to take each of these exams at least three times to guarantee a pass, and while I only managed to take each one two or three times, I felt very prepared if not overprepared for the real exam. The questions are mostly solvable if you took the class, but he throws a few curveball questions at you that he did not cover at all (similar to the exam) and this is where having your additional reference really helps. All of the exams, especially the hard and very hard CBTs, had a few lengthy questions that were very difficult to solve within the time limit or required you to envision invisible triangles and know your trigonometry inside and out. However, by taking the exams over and over and learning from your (sometimes repeated) mistakes, you can finish even the very hard exam with time to spare.

Recommended Calculator
Kirk highly touts the TI-89 calculator for this exam because of the easiness of using answers from previous calculations and its DMS buttons.  Speed is the name of the game, and he even shows you how to use the calculator’s functions in addition to solving practice problems with it.

The TI-89 is indeed a fine calculator, but unless you already have it, I don’t recommend buying it for three reasons. First, it’s pretty expensive at roughly $130 online. Second, the TI-89 is not allowed for the National Civil PE Exam. But more importantly, entering DMS angles on it is a bit cumbersome compared to my favorite calculator, the Casio fx-115ES PLUS (only $16!). I’ve actually written a post on this topic if you’d like to make an informed decision for yourself. Either way, you’ll be fine taking this class and the exam with or without the recommended TI-89 calculator.

The 12 instructional hours you get from the CPESR course videos are relatively short, but the quizzes and CBTs are where you get the most bang for your buck. I truly believe that there is enough variety of questions in the CBTs that if you can learn to comfortably answer each one in all of the CBTs, and bring another reference, you will find that the real exam is a piece of cake.

I did not have any experience in surveying before taking this course besides looking at construction plans and skimming through Cuomo’s Surveying Principles for Civil Engineers (which is a good starter book for surveying newbies). However, when I took the real exam I finished early and felt that it was on par with the difficulty level of the “very easy” to “normal” CBTs offered by CPESR.

CPESR prepared me well for the CA Surveying exam and passing on my first try, and I would recommend it to anyone considering it for their exam preparation.

Culverts: The Ponded Condition Assumption

When analyzing culverts, a pooled condition, or zero approach velocity, is typically assumed at the inlet, which results in an appreciable amount of headwater. This is reasonable since a culvert’s opening is usually very small compared to the upstream cross-section (e.g. a natural watershed or wide channel) and water has to “slow down” or “wait in line” before it can flow into the culvert.

The Hallway Analogy
To visualize the ponded condition, picture this scenario: You’ve just finished watching a concert, and now it’s time to head home. You and a crowd of people are walking down a hallway, and there’s only one door at the end. Of course, it’s going to take a while to get out since only one person can go through at time. You have to slow down and wait for the other guys to go through. This is how water behaves in the ponded condition, more or less; not only is there a backup of people at the door, but you had to stop walking altogether due to that backup. In other words, your approach velocity is zero, and the backup of people represents the headwater depth.

Now, imagine the same scenario, except the hallway has wide, sliding doors, and perhaps a tapered entrance. Here’s how that might look:

Although both analogies makes us look like a bunch of sheep, this hallway obviously lets more people through, resulting in less of a backup and allowing you to maintain your pace, or approach velocity. When it comes to culverts, they pretty much behave the same way.

Ponded Condition in Real Life
Ponded conditions may or may not exist for a culvert, but it’s normally assumed since it’s a worst-case scenario and makes calculations much simpler. However there are actually many cases where there is an appreciable amount of approach velocity. For example, if there is a channel that facilitates flow into the culvert, the approaching water will preserve much of its kinetic energy as it passes through. As a result, there’s less energy lost and this results in a lower headwater depth (or “backup”) than that calculated if pooled conditions were assumed.

Here’s an example of a culvert that would have a good amount of approach velocity that probably shouldn’t be neglected, especially at lower flow conditions (if anybody is willing to send or refer me a better picture than this, I would greatly appreciate it! I only have pics from wikicommons at the moment):

Photo © Michael Trolove (cc-by-sa/2.0)

Now compare the above culvert to the one below, where the upstream end isn’t as channelized and the approaching water appears tranquil:

Photo © Bonnachoven (cc-by-sa/1.0)

And here’s an extreme example of a culvert where there would definitely be ponded conditions in most cases:

Photo © Peter Ellis (cc-by-sa/3.0)

When NOT to Neglect Approach Velocity
The above pictures give you a nice visual of when the approach velocity is and isn’t significant, but it’s not always clear when you should neglect it. It’s your judgment call, but the approach velocity should generally be included in calculations if:

  • There is a channel that directs the flow smoothly into the culvert at design flow (similar to the first picture above)
  • The area of the approach channel to the culvert is less than five times the area of the culvert barrel (per a USGS report1)
  • The culvert is large enough to have free surface flow all throughout the barrel (no backed up water at all), or if the culvert can be considered a bridge.
  • The culvert is part of a larger storm drain system, or if you’re required to model the water surface profile throughout the culvert or entire system
  • There are significant effects from upstream or downstream drainage structures
  • The culvert is used as an irrigation structure
  • The culvert must incorporate aquatic organism passage (AOP)

This isn’t an exhaustive list, but if your culvert falls into any of these categories, you would be better served using software that performs gradually varied flow (GVF) calculations to carry the water surface profile through the culvert. HEC-RAS and WSPG are a couple of popular programs that can do this.

It’s generally safe to assume zero approach velocity since you’ll always calculate a more conservative (higher) headwater depth. The nomograph solutions for culverts and the FHWA’s HY8 culvert program make this assumption, and it’s perfectly reasonable.

The “ponded condition” assumption is a simple one, but hopefully my explanation made sense. As always, there are disclaimers and exceptions when modeling the flow of water, so I may not have covered everything here.

*I highly recommend reading the FHWA’ culvert design manual (HDS-5) or taking a look at this Youtube video they published if you want to learn more about culvert hydraulics.

1 Computation of peak discharge at culverts. Ronald William Carter. US Geological Survey, 1957.

Solids Concentration: Why does 2% solids equal 20,000 mg/L?

A common way of describing the thickness or “soupiness” of sludge is % solids. Percent solids is a measure of the amount of solid material in a wastewater sample. As this number increases, the sludge becomes less watery and thicker to the point you can hold it in your hand (with gloves of course). You’ll commonly come across this measurement if you’re ever doing any problems involving anaerobic digesters, sludge thickening, or dewatering. Here’s the difference between sludge’s consistency at different % solids:

2% solids sludge collected from an anaerobic digester.

Dewatered sludge at around 15 – 25% solids.
Also known as “cake” or biosolids. Smells pretty earthy.
(Photo credit: Sustainable Sanitation Alliance / CC-BY-4.0)

While percent solids is a nice way of describing solids content, it’s not readily useable for most wastewater calculations. Wastewater problems typically will require you to convert % solids to mg/L in the beginning. Luckily, the conversion is simply:

1 % solids = 10,000 mg/L

Therefore, 2% solids equals 20,000 mg/L (soupy), 15% solids equals 150,000 mg/L (thicker), and so on.

But something that bothered me for the longest time is why 1% solids equals 10,000 mg/L, and not simply 1000 mg/L or anything else for that matter? The answer is that going from % solids to mg/L is a units conversion. It’s a simple conversion, but I’ve never seen this covered in a textbook, so here’s an example of the conversion below:

1.) For poop’s sake, let’s assume we’re working with 2% solids. We know 2% solids is another way of saying 2 lb solids/100 lb wastewater (English) or 2 kg solids/100 kg wastewater (Metric). This is always true, unless the problem specifically states that % solids is on a volumetric basis (for the P.E. exam this isn’t likely).

2.) The next step is to convert this to mg/L using the density of water and any relevant unit conversions:

(English Units)
(Metric Units)
*Note: The wastewater (sludge), consisting of solids and water, is assumed to have the same density as normal water (1 kg/L or 62.4 lb/ft3), but this isn’t strictly true.

And that’s it! Just clever manipulation of the units. Whenever you see % solids, multiply that number by 10,000 to convert to mg/L., and vice versa.

EET Seismic Principles Course Review

I want to write an honest review about the Seismic Principles exam prep course offered by Engineering Education and Training (EET), and taught by Ahmed Ibrahim. After much practice and dedication, I passed this exam on my first try thanks to Dr. Ibrahim. I cannot say enough good things about this course or professor.

The Seismic Principles exam is a 2.5 hour, 55-question computer based exam offered by the California Board for Professional Engineers, Land Surveyors, and Geologists (BPELSG). This test is no joke, especially for those with a non-structural focus, since you need to understand some pretty complex concepts if you want to pass. Also, at roughly 2.7 minutes per question, with many of them requiring you to lookup information in various references, you can’t afford to make many mistakes. If you have no structural background like me, you absolutely CANNOT self-study for this exam.

EET’s course was recommended to me by many people at engineerboards.com and my coworkers, so I decided to give it a shot.

The course was $500 when I took it, and includes everything I’m discussing below. It sounds like a lot, but you really get your money’s worth.

Lecture Quality
EET offers their seismic course in a live (in-person or online), and on-demand video format. I took the on-demand version, and it’s nice that you can rewind when necessary and view the videos whenever you want. The on-demand course uses recorded lectures from the previous online class. The courses and other content are accessible through a browser-based software called Adobe Connect.

In total, there’s about 60 hours worth of video content, and you can view the videos as many times as you’d like. In the videos, Ahmed goes through each page and example in the provided textbook, and adds tidbits of comments and extra examples to help you understand the concepts. There’s also a chatroom where you can ask questions or post answers to Ahmed while he’s teaching (in the on-demand course you can still view the chatroom).

To me, Ahmed’s commentary was the most useful. Dr. Ibrahim lets you know what you should highlight or make extra notes on. He also goes over common mistakes, and what is likely to appear on the exam. He’s an expert on the subject, so there are some extra topics that are in the book for completion’s sake, but are not necessary. However, he knows this and he makes sure you focus on what’s important for the exam.

Class Textbook
Ahmed has actually written a textbook for studying and preparing for the Seismic Exam, and it provided in the course package. The book assumes you have no prior structural experience, and starts from learning about what causes earthquakes, to calculating the shear capacity of a wooden diaphragm. The book is too dry to read on your own, and is a bit theoretical, but the class lectures are entirely based on the book, so if you just follow along with the course videos, you’ll be able to go through the entire book. There are 14 chapters in my version of the book, and at the end of each chapter there are anywhere between 10-150 practice problems, along with an appendix containing the solution to each one. The book comes in a comb-binding, and you’re allowed to bring it into the exam room.


Reference Materials
I’m no structural engineer, but from how I understand it, in California, building design is based on the California Building Code (CBC), which has adopted much of its regulations from the International Building Code (IBC), along with some amendments. The CBC includes seismic design requirements. Many of these seismic requirements are based on a document published by the American Society of Engineers (ASCE), called the “Minimum Design Loads of Buildings and Other Structures” or ASCE-7. Most of the equations/design criteria on the test are based on ASCE-7 and the CBC. Some other organizations, such as The Masonry Society and American Wood Council, have their own design criteria for their respective building materials.

ASCE-7 Cover

It’s quite daunting how much reference material you need to have on-hand for this exam. Thankfully Dr. Ibrahim provides you with all of the necessary codes, equations, and references you need. You absolutely do not need to print or buy anything else beyond what’s provided by the course.

Here are some photos of my reference binder that includes all of the reference materials provided by the course. I used this binder to answer about 90% of the questions on the test, while using the book’s index for anything I couldn’t find. Please note that you really need to know all of your references inside and out for your binder to be effective. I highly suggest writing your own personalized notes and adding tabs so that you can quickly lookup information.


Practice Quizzes/Workshops
The course also provides you with “workshops” and practice-quizzes. The workshops are PDF/printable and contain additional questions with step-by-step tips for solving the problems. After solving the workshops you can look at a video where Ahmed covers each question in depth.

The practice quizzes come in PDF/printable form and are useful for gauging your mastery on chapters with tough concepts. Questions on these quizzes are for the most part much harder and longer to solve than the actual exam’s difficulty. These practice quizzes come in handy as an additional study tool to the CBTs.

Computer-Based Tests (CBTs)
The CBTs give you a good feel for what the exam day will be like. Ahmed’s course is setup so that you complete the entire book, videos, practice-quizzes, and workshops before you take the CBTs. He recommends you take the CBTs starting the week before the exam, and its good advice because it gives you enough time to prepare mentally for the big day.

The CBTs run on a software that is very similar to the one used at Prometric (the testing company that administers the test) . There’s a countdown timer and you can flag questions. However, I believe one of the features that were missing in the CBTs versus the actual test is the ability to cross-off eliminated answers by clicking the right mouse button.

There are three CBTs, ranging from (1) tricky, (2) lengthy, to (3) about-what-you-should expect. I’d say that all of these exams, including the third one, are a good representation of the actual exam difficulty. You can take the CBTs over and over until you master them.

After completing the test and wiping off the exam sweat, you get your score right away. The answers are not online, but instead they are in a solutions booklet that is provided in addition to the class textbook. I believe you can buy this booklet separately on Amazon if you don’t plan on taking the full course:

The Teacher
Ahmed is a very dedicated teacher, he really knows his stuff, and he truly wants you to succeed. He responds fast to emails, has online office hours every week, and even provides you with his phone number.

Just to give you an example of Ahmed’s dedication, after I took a couple of the CBTs and did pretty well on them, he personally emailed me to comment on my good scores and offered words of encouragement. Who does that?! Keep in mind I was taking his on-demand course, so I didn’t really interact with him besides emailing him a few times for help on a few tricky textbook questions. Ahmed really made me feel like his actual student, and not just another customer.

Closing Notes
The actual exam turned out to be tougher than the CBT exams, but since this was the first CBT exam I ever took, I think stress and nerves got the best of me (tip: don’t wear headphones to block out the noise, you’ll end up hearing your heartbeat and psyche yourself out). I really, and foolishly, believed I would be able to ace the exam after my past performance on the CBTs, but I ended up completely guessing on seven of the problems since I ran out of time. My confidence was shaken as I left that exam room, but I still thought I answered enough questions correctly to pass (and I did!). The preparation I received through EET instilled hope that I would pass regardless. Ahmed also offered encouraging words after the exam.

I had a great experience taking EET’s Seismic Course, and I highly recommend it to anyone. You’ll have very good odds of passing if you complete his entire course, practice problems, and CBTs, regardless of your background. In fact, when I took the exam in Spring 2017, the reported passing rate was 89% for all of his classes. I believe that as long as you put in the time and effort to train with EET’s course, and follow Ahmed’s advice, you will very likely pass on the first try. Thanks again Dr. Ibrahim!

Watercourses and ridges on topographic maps: Why the V’s?

*If you’re not familiar with topographic maps, I recommend going over this National Resources Conservation Service (NRCS) article on reading topo maps first.

Why does a “V” point uphill for a watercourse, and downhill for a ridge?
When viewing topographic maps, you’ll notice that valleys or watercourses are always shown in areas where a V’s pointy end is oriented uphill. In contrast, mountain ridges are in areas where the “V” points downhill. “Just look for the V’s” is common advice when looking for these features.

Note: This topographic map is from the USGS’s official website, on their GIS map viewer.

Why’s it got to be a “V”?
To me, this advice is not intuitive at first because valleys and ridges do not always look like a “V”. Sometimes they can look like really flat, subtle “U”s. It’s also easy to mistake one feature for the other if you just look for the “V.” What’s so special about the Vs?

The 90° rule
A better way to interpret topographic/contour (line of constant elevation) maps, and to understand why “V”s are indicative of valleys and ridges, is the following rule: “Water always flows downhill, perpendicular (at a 90° angle) to contour lines.” Seriously, if you can remember this, you can understand how water will flow in any area, with or without any obvious “V.”

Take a look at this contour map below. The left side shows a valley (watercourse) and the right side shows a ridge, or watershed boundary. Now, imagine it’s raining uniformly over this entire area. The blue lines show where raindrops will flow to once they hit the ground and gravity takes over. These blue lines follow the 90° rule:

If you can follow this example, you can figure out the drainage patterns of any topographic map you view, especially since most maps have contours going all over the place. To be fair, even for the less-obvious ridges or valleys you’ll be able to find a “V.” However the “V” may be very wide (flatter), or may have a lot of curves resembling a sine wave.

Here’s a USGS topographic map of an area with some obvious watercourses, and a well-defined ridge (in red) at the bottom. This area slopes downward to the west. Points A and B are for reference. Notice how there is vegetation from east to west. Vegetation often coincides with a well-defined watercourse.

Note: These modified topographic maps and imagery are from the USGS’s official website, on their GIS map viewer.

And for a better view, here’s a Google Earth version (looking easterly):

Map Data: Google,  INEGI

I hope this helps! Remember, the 90° rule can hep you in any rainy-day situation…Bah dum tss..

Applying Manning’s Equation to Pipes

Does Manning’s equation work for pipes, not just “open” channels?
Yes! As I’ve previously discussed, Manning’s equation can also be used for pipes, as long as there is a free, exposed water surface. The area and wetted perimeter are hard to calculate, but doable if you utilize the graphs that relate circular pipe ratios (D/Dfull, Q/Qfull, etc.). Here’s Manning’s equation below:

(English Units)

Note: If the pipe is pressurized, then Manning’s equation should not be used, but there’s one exception. You can actually use Manning’s equation for a pipe flowing just full, but not technically pressurized. The assumption is that the pipe has just barely become full, and that any additional infinitesimal flow would make the pipe pressurized. The discharge of the pipe in this condition is usually called Qfull or Qfull capacity. Qfull is actually extremely important, because a pipe flowing under the Qfull condition has less discharge than a pipe flowing just below the full depth (a circular pipe conveys the most flow at about 94% of its full depth). The reason why Qfull is less than Q94% depth is because even though there is more flow area in the full-condition, there is even more friction (wetted perimeter) gained as a result of the pipe closing in on itself. This additional friction cancels out the additional flow area and slows down the water.

Take a look at this example to see how this concept applies to a nine foot pipe:

If you still can’t believe this is true (because I definitely didn’t at first!), check out this graph and look for where Q/Qfull is maximum:

Note: This graph assumes “n” does not change with depth.

Qfull is actually pretty usefull (pun intended). At work, I use a popular program called Flowmaster to calculate Qfull. During the beginning, planning stages of sizing a pipe, I’ll use Qfull to get an idea of my pipe’s maximum capacity rather than Q94% depth. Qfull is a safer number to use since there’s always a chance the pipe will seal up with water, especially if there’s a clog in the system or backwater effects.

But remember, gravity-drained systems, such as storm drains, should not be designed solely on the basis of Qfull. A more detailed hydraulic analysis, utilizing the energy equation and a whole lot of iterative calculations (standard-step method) is usually needed, especially if there are any transitions to different-sized pipes, tight curves, abrupt changes in the slope, and/or the pipe becomes pressurized.

As a shortcut for the PE exam, here’s the formula for calculating Qfull in a circular stormwater or sewage pipe. If the pipe is not full, use the circular pipe ratio graphs to calculate A and R for use in Manning’s equation:

(Circular pipe; English Units)

Open Channel Flow – Manning’s Equation

(English Units)

Manning’s equation is perhaps the most popular formula for open channel flow. You can calculate the flow and velocity (Q/A) of a channel or non-pressurized conduit, such as a circular pipe, using this equation.

This formula can also be rearranged to solve for the normal depth (yn) of an open-channel, such as a rectangular channel:

(rectangular channel; solve by trial & error)

 Here’s a summary of each term below:

Q: Flow, a.k.a. discharge (cfs)

n: The Manning’s “roughness” coefficient of the channel. This value shows how much resistance is acted upon the water by the channel. A lower n-value means less roughness, and usually implies a higher velocity and smaller depth in the channel (and vice-versa), with all else being equal. Concrete, which is valued for its hydraulic “smoothness”, has an n-value between 0.013-0.015. For comparison, a natural stream with little to heavy vegetation can have an n-value ranging anywhere between 0.025 to 0.150. Now just imagine riding your road bike on concrete vs. a grassy field, and which surface is much easier to ride on. That’s how the water feels.

A: Flow area (ft2) (Note: not necessarily the full area of your channel section!). For example, if a rectangular channel is flowing half-full, the area would be the base x ½ height, not base x height.

w: width (base) of a rectangular channel (ft).

R: Hydraulic radius (ft), or R = A / P. P is the wetted perimeter, or the length of water that is in contact with the physical channel (i.e. receiving friction). For example, in a rectangular channel flowing half-full, wetted perimeter is the base plus the length of both vertical sides touching the water (see equation above).

S: Technically it’s the friction slope (Sf), but for most applications (and on the P.E. exam) it is the channel’s slope, in decimal form (e.g 0.003 or 0.2). Channel slope is assumed because the prime assumption of Manning’s equation is that the channel is flowing under uniform flow. In uniform flow, the gravitational forces (i.e the weight of the water) cancel out the frictional (resisting) forces, which causes the friction slope to equal the channel slope (Sf = Schannel). Do an energy balance calculation between two points on a uniform-flow channel and prove it to yourself (I will cover this in a more nerdy, in-depth discussion of uniform flow in the near future)

yn: Normal depth (ft), or the depth of flow the water would normally take in the channel assuming there are no changes in the channel’s shape, friction, or backwater effects in either the upstream or downstream direction from the channel for a good distance. In other words, this is uniform flow, as will be discussed in a future post.

Manning’s equation can also be used for non-pressurized pipes, or those flowing with an exposed water surface, as I’ve discussed in a separate post.

P.S. A shoutout to Conrad at ReviewCivilPE.com. I don’t think he updates his site anymore, but his article on Manning’s equation inspired mine!

The Coordinate Method – Explained, with a Shortcut

Per the CA BPESLG’s test plan for the civil surveying exam, test takers need to know how to perform “trigonometric relationship to determine the area of a polygon” and “procedures for calculating area” when it comes to traverses. If you’re taking a course or self-studying, then you’ve probably heard of these three methods for calculating the enclosed area of a traverse/polygon:

  1. Divide the traverse/polygon into simple triangles and/or parallelograms.
  2. The double-meridian-distance (DMD) method
  3. The coordinate method

In my opinion, the easiest way to calculate the enclosed area of a traverse is the coordinate method, since it is simply a plug-n-chug problem (so is the DMD method, but it has more rules to follow) if you’re given coordinates or can easily resolve the polygon’s vertices into a coordinate system.

So, let’s take a look at the coordinate method formula for a 4-sided traverse with points A, B, C, and D:

What the heck? At first glance, this doesn’t seem like a simple plug-n-chug formula. Also, why is YA reintroduced at the end, and why is YD in the beginning term? The formula looks pretty daunting, but here’s a better way to visualize what’s going on in that nasty numerator (this figure was inspired from Chapter 6.8 from Cuomo, 2nd edition)

The products of the solid lines are positive, while the products of the dashed lines are negative (compare this to the previous formula to confirm). From this diagram above, you can see pretty clearly why the coordinate method is also called the “criss-cross” method, since you must go around the traverse, coordinate-by-coordinate, and multiply by the coordinates before and after by the one you are currently working on. You’ll notice that I have highlighted (XA, YA) in red and (XD, YD) in blue to illustrate this point. If you were finishing the calculation, you would have to multiply Point D’s x-coordinate with the y-coordinates from Point C, and Point A (the beginning point).

If that explanation confused you, don’t worry, there’s a a shortcut to this madness and no need to recall any formula!

(Somewhat of a) Shortcut to using the Coordinate Method

The best way to calculate an area using the coordinate method is by setting up a table for your criss-cross calculations. Instead of giving you a list of steps, I’ll show you an example:

Question: What is the area of the 4-sided traverse below?


Step 1.) Resolve the traverse or polygon into (x,y) or (N, E) coordinates: You’ll see that I was nice and gave you the coordinates already, but if you’re not given any coordinates and it’s too complicated to resolve the polygon into triangles and rectangles, make up your own coordinates for each vertex (it’s nice to label one of the points strategically as (0,0) to ease calculations).

Step 2.) Create a two-row table, with as many columns as there are unique points , plus one more (in this case 4 +1 = 5).  The top row is for x-coordinates, bottom row is for y-coordinates. It really doesn’t matter which row you use, or if it’s Northing and Eastings, but what does matter is that you must write the coordinates in order, going clockwise or counterclockwise, starting at any vertex. Also, you must enter the same coordinates you started with in the last column (in this case point A was entered in the first and last columns).

Step 3.) Beginning with the first column and moving right, do a “criss-cross” calculation for the top row. In other words, multiply the first column/first row by the second column/second row, and write the answer underneath (shorthand notation for big numbers). Continue this for each column, moving right.


Step 4.) Do your “criss-cross” with the bottom row, writing the answer on top:

 Step 5.) Calculate the sum of the top and the bottom. Be sure to include negative signs in your summation when you have negative coordinate(s).

Step 6.) Take the absolute value of the difference between the sum of top and sum of bottom. Divide this number by 2, and that’s your answer.

The above process worked well for me on the exam, and it’s pretty fast once you get the hang of it. Hell, as long as you set up the table, you could probably do all these calculations in one or two steps on your calculator. The table just helps you visualize the sequence.

If you liked this “shortcut”, here’s what I would recommend writing in your references to help you remember the process:

Four a four-sided (for simplicity) traverse/polygon, with points A, B, C, and D:

Seismic Terminology: Story vs Level vs Floor

One of the most common mistakes  I’ve heard of people making while studying for the seismic exam is the difference between story, level, and floor. While in everyday life these words are interchangeable, they have specific meanings for the seismic test. Unfortunately they’re very easy to mix up!

For example, think in your head where on the building below you would analyze to answer the following questions (assuming you’re given lateral forces and deflections at each level):

1.) What is the shear force just below the third floor?
2.) What is the story drift in Story 2?

For Question #1, if you analyzed the forces below the green line (which is actually the fourth floor), you would be incorrect, and this would likely be a trick answer on the exam. The correct area to analyze is the space below the blue line (third floor, or second level). Remember, although the ground doesn’t have a horizontal line, you cannot forget about it! The ground is defined as the first floor, or level zero. So count your way up from the ground to figure out the numbering.

Question #2 is a bit easier, the correct way is to compare the story deflections between the red line and blue line. However, I know when I began studying I confused “story” with floor/level, and didn’t even know where to begin due to this mixup.

In basic terms, here’s how I define the differences between story, level and floor:

Level: Surface that begins at level zero at the ground
Floor: Surface that begins as the first floor at the ground (think of an elevator)
Story: The ­space between the levels/floors that you would occupy if standing inside the building. Begins at story 1 between levels 0 and 1, or floors 1 and 2.

For your studies, I highly recommend jotting down your own diagram of the differences between these terms for your references. Here’s a sample diagram I drew up:

What’s the best calculator for the CA Surveying Exam?

While studying for the surveying exam you’ll notice that most problems will give you an angle in terms of minutes, degrees, and seconds (aka DMS; e.g. 5°36’46”)In most cases this is no big deal, but during the computer-based exam when you’re pressed for time and the clock’s ticking you need all the help you can get to increase your speed. Not only that, most problems will give you numerous DMS angles where you have to add a lot of things up.  I understand the importance of DMS since it is more precise than decimals, but it can get pretty frustrating smashing your calculator buttons for what seem like an eternity just to enter one angle!

Luckily, I believe there is one calculator that stands out above the rest when it comes specifically to the surveying exam, and that is the Casio FX-115 ES PLUS (and yes, its allowed on the national and CA specific exams). Why? Because of this button right here:

With just one push, this button lets you enter the degree, minute, second AND convert back and forth between DMS and decimal degrees. There’s no need to scroll to a menu or press any additional buttons, and trust me this is a lifesaver! I’ve recently taken the April 2017 CA surveying test, and my biggest worry was my speed. I honestly believe this button saved me a good 5 minutes on the 2.5 hr , 55 question exam . Yes, this is a big deal!

While it may sound like I’m some Casio representative, hear me out: I was a Texas Instruments (TI) man my whole life, and my calculator of choice had always been the TI-36x Pro  Also, I took an online surveying preparation course and the teacher really recommended the TI-89 Titanium (which I already owned) for its ability to enter DMS angles quickly. However, I noticed that while both calculators are superb for normal calculations, entering DMS angles is very clunky on both. On the TI-36x pro, I have to scroll to a menu (e.g 2nd -> Math -> scroll to DMS -> degree /minute/or second) each time. On the TI-89, it’s just 2ND-> degree/minute/or second, but still, why should I have to poke my calculator twice if I don’t need to? On the FX-115, all I need to do is press that one button and I’m golden baby.

Here’s my demonstration of adding 5°36’46” and 1°33°37 on the three calculators above. See for yourself how easy it is on my FX-115 ES PLUS:

It took me 7 seconds to do this calculation on the FX-115 ES versus 12 seconds on the TI-89, and 18 seconds on the TI-36x Pro.  If we compare the time it takes to complete this problem between the FX-115 ES and TI-89, I save at least 5 seconds by using the FX-115 instead of the TI-89 for each calculation . Assuming 20/55 (conservative, like us pesky engineers always are) of the problems involve 3 simple calculations (what if you had to do a 5 sided closed traverse?) like the video shows, you could save about 5 minutes on the exam. 5 minutes doesn’t seem like a lot, but this is enough time for you to quickly checkmark your unanswered questions or check on previously solved problems.

My coworker recommended and let me try out his FX-115 ES since I asked him for tips on improving speed, and honestly as soon as I touched that amazing button I had it in my Amazon shopping cart within minutes!

You’ll be okay with either TI calculator (even HP) if you are used to them, but I really do recommend the FX-115 ES PLUS (and the original ES), not just for the surveying exam, but also for the seismic and national exams. It’s just as responsive as the TI calculators, and it’s also very easy to enter and solve complicated, iterative equations, or even just the quadratic formula. Plus the FX-115 ES is only $20 (as is the TI-36x Pro), while the TI-89 is about $120 brand new. One thing I did notice is that it slides a bit when you’re punching numbers, but it’s not a dealbreaker, especially when you have that adorable but lifesaving DMS button!

P.S: Here’s a link to Turbofuture’s (tech review site) concise review of the Best Calculators for the PE Exam which partly inspired me to write this post.