Posted on Jan 18, 2021
Ryan Nicoll

Why free body diagrams eliminate confusion in engineering design

Originally published on

There is a small town on the border of the Netherlands and Belgium that has an identity crisis. That’s right – it’s not only people that can have existential angst but a physical town, too! This town is split between the Netherlands and Belgium – literally. The problem stems from hundreds of years of historical treaties that left land traded back and forth between the countries, resulting in a completely bizarre border.

You would think it would be bad enough that the border zig-zags through the town. But worse, it actually makes a series of pockets of one country or the other sprinkled throughout the region. It’s so intricate that even houses are split in two, straddling the nations. You can imagine not knowing which country you are in just by crossing the street. Without a map, you’re left not really knowing where you are, and it can leave you dizzy with confusion.

The border between the Netherlands and Belgium at the town of Baarle Nassau / Baarle Hertog cuts through town in very strange ways.

Likewise, many hydrodynamics problems can leave you feeling dizzy with confusion at first glance. There can be many complex effects involved and it is easy to lose track of what’s going on. This article will discuss how free body diagrams act like a map to keep things organized and help eliminate that confusion. We’ll also use free body diagrams to introduce how buoyancy and drag are key forces in oceanographic mooring design.

A free body diagram comes in to play when we want to understand forces acting on a structure

A ship moored in a storm presents a complex scenario. There may be one or more hulls – ships or buoys – or both – and interconnected mooring lines. There are complicated forces involved caused by wind, current, and waves all happening at once. We use a free body diagram to isolate one entity and one entity alone in the scenario. Isolating this one body, we lay out all the forces acting on it from the environment onto the body itself.

Laying out the forces in a free body diagram is the first step in understanding the problem

Once you understand the problem, you can start solving it – that is – understanding the motions of the system and the structural forces involved. This will help you know if your ship is likely to capsize or if your mooring lines are likely to break or not in these harsh ocean conditions.

There’s more than one way to use a free body diagram

But ultimately, the first step is isolating the body you want to look at in more detail. Once you have that body isolated, you then need to show all the forces acting on it from the environment.

Once you have all the forces laid out acting on the body, you need to resolve the forces from each source. The balance of the forces acting on the system will tell you more information on the structural loads, the accelerations involved, or both.

When do we use free body diagrams?

When you are looking at a new system for the first time, it’s a good idea to draw one out to get an idea of what’s happening. If you don’t have a specialized software tool that solves these problems, it’s a free body diagram is an essential way to get an initial understanding of the problem.

Free body diagrams help understand what’s happening in problems like subsurface mooring design in an ocean current.

But what if I miss a force in my diagram?

Free body diagrams can also be handy to validate your assumptions. If you measure something in reality – like a mooring tension from a system at sea – writing down the balance of forces you know about in a free body diagram is essential to help you understand if you’re missing something or not. This is especially important if there are significant differences from the software tool you’re using to design a system when compared to what you see in reality.

It’s time for an example

Free body diagrams can be an abstract concept without grounding them with a specific example. In this example, we are going to look specifically at the main float of a subsurface mooring. We’ll make some assumptions on this problem to keep it very simple. It is in a steady state, so there’s no motion, only a deflection of the taut mooring line in the current. Let’s draw a free body diagram of the subsurface buoy.

Figure 3: The forces acting on the top float of a subsurface mooring are buoyancy, drag, weight, and mooring line tension.

There are a lot of complicated effects happening in what may look like a simple scenario. There is a hydrodynamic drag force acting on the float from the current. There is buoyancy pushing up on the float and gravitational weight pulling down. The mooring reaction load comes off at some angle to restrain the whole system.

We can characterize the environmental forces – weight, buoyancy, and drag. Once these are known quantities, computing the balance of forces acting on the float reveals the only remaining unknown – the line tension. Since this tension comes from the mooring line, it will show us what angle the mooring line is at and the magnitude of load. Knowing the magnitude of the tension means we can make sure we have the correctly sized rope for the problem.

This is a very simple example to show what it might look like when laying out the forces. But the goal isn’t to overwhelm with details here. This kind of evaluation is done behind the scenes in software tools like ProteusDS Oceanographic to help you resolve the correct size of mooring components to use.

It’s time to review

Free body diagrams help you focus on one specific element in a problem. You pick one body and draw out all the forces acting externally on it. Primarily, these will be environmental forces like those from wind, waves, and currents. This is the first step in breaking down the problem and resolving structural loads and motions – and it is a concept that is at work behind the scenes in software like ProteusDS Oceanographic. A free body diagram will also help you find out if you’re missing something when you validate your understanding with measurements from real systems. You can even directly solve some simple systems – like our example of a subsurface mooring.

In some small towns straddling Belgium and The Netherlands, the border is so convoluted you may lose track of which country you are in as you cross the street. A map is a must to help reduce confusion. In hydrodynamics problems, a free body diagram is very much like a map that helps reduce confusion.

Next step

Buoyancy is one of the most important forces in any kind of design for marine structures. Read more about where it comes from and common mistakes when designing oceanographic moorings here.