🔍 Decoding Dr. Förster's Field Strength Blueprint for Modern Eddy Current Testing

If you’ve ever stared blankly at some of Dr. Förster's impedance graphs, you’re not alone. There is a treasure-trove of information locked up in Dr. Förster's charts and graphs, and when properly decoded, they will surely help empower you to knock that imposter-syndrome ET monkey off your back!

This iconic spiral of vectors in Figure 1 doesn’t just look impressive—it’s the Rosetta Stone for understanding field strength distribution in cylindrical test objects. And yes, it still matters—a lot—in modern eddy current testing.

Figure 1

So What Is Figure 1 Showing?

At its core, Figure 1 plots the amplitude and phase angle of magnetic field strength as a function of depth inside a solid cylindrical conductor, like a rod. The radial position (from surface to center) is shown as a fraction of the cylinder’s radius. Each curved line represents a different frequency ratio f/fg where:

• f = test frequency

• f g ​ = material-dependent “limit frequency” (Dr. Förster's signature secret scaling factor).

  
  

The vector length shows how strong the magnetic field is at that depth. The vector angle shows the phase shift as you go deeper.  If you pick two adjacent spirals (one higher f/fg  and one lower f/fg ), and follow their paths counterclockwise towards the center of the solid cylinder, you will see that the higher f/fg ratio (higher test frequency) exhibits more phase lag as the magnetic field strength and eddy currents weaken as they travel towards deeper depths. 

And if you can recall hearing about “center effect” from your classroom instruction, that’s exactly what’s happening at the center cylinder, all eddy currents are cancelled. And just to be clear (hopefully), the smallest concentric circle towards the lower-right hand portion of the graphic does NOT represent the center of the cylinder, it simply represents the termination point of the loci. If one were to "zoom out" and look at the loci in their totality, they would all eventually terminate at the center of the smallest concentric circle, where magnetic field strength and eddy currents are kaput.

Below are some tips to help you decipher Figure 1:

Element	What It Represents
Outermost start of spiral	Surface of cylinder (field = 100%, phase = 0°)
Spiral path inward	Deeper field penetration + growing phase shift
Inner end of spiral	Max depth reached at that frequency ratio
Vector angle	Phase lag of field vs excitation
Vector length	Amplitude of field strength
Labeled radii (0.9, 0.8, ...)	Percent of radius from center, .9= 5% depth from the OD, .6= 20% deep from the OD, etc.

Why Did Dr. Förster Develop This?

Dr. Förster was a physicist obsessed with precision. He needed a way to:

• Quantify how deep eddy currents and magnetic fields penetrate.

• Model how test frequency and material properties impact inspection depth.

• Support a similarity law: if two materials have the same f/fg ​, their internal field behavior is nearly identical.

With this, he could predict what a flaw signal might look like—even without touching the part.

How Did He Use It?

Dr. Förster was modeling ET behavior, the results of which help us today in understanding eddy current depth of penetration and phase lag.

Figure 1 was critical for:

• Selecting optimal test frequencies

• Predicting where flaws could (or couldn’t) be detected

• Designing experiments with mercury-filled cylinders and tiny coil probes to validate the math.  (How else do you think Dr. Förster got all those tiny discontinuities in the middle of solid cylinders??)  He positioned small nonconductive objects into the desired position within the column of liquid mercury.  It has not been verified by the author if the German equivalent of OSHA was a thing back in Dr. Förster's lab or not.

This was the beginning of true quantitative eddy current testing—long before digital instruments.

Why It Still Matters Today

Here’s the kicker: this isn’t just historical fluff. The math behind Figure 1 powers today’s:

• Crack sizing algorithms

• Depth-of-penetration settings on flaw detectors

• Lift-off compensation logic in array probes.

In fact, if you use tools that auto-adjust frequency based on part diameter and conductivity—guess what? You’re standing on the shoulders of Figure 1.

Practical Example for Today’s Analyst

Let’s say you're inspecting a 1.2 cm aluminum rod at 10 kHz. If your f/fg = 100, you’re mostly seeing surface features—the field dies off quickly. In Figure 2, the author demonstrates with a slide rule that the standard depth of penetration for aluminum at 10 kHz is roughly 1mm (look at the second scale below the inverted black triangle).

Figure 2 (Ed's Slide Rule)

But at f/fg ​ = 5? You’ve got deeper penetration—but diminished crack resolution. This trade-off is visible at a glance in Figure 1.  In Figure 3, the author demonstrates that using 500 Hz increases the depth of penetration by approximately 4X, which validates Förster's foundational work was spot-on.

Figure 3 (Ed's Slide Rule)

It’s one of the clearest ways to teach students the balance between sensitivity and penetration—without dragging them through differential equations. An even easier route is to make your own calibration block- drill some holes from the bottom up towards the surface; grab a tester and a wide surface probe, start playing around with test frequencies and graph your results.  I can already tell you how that’s going to turn out 😊.

Want to Learn More?

If you’re an analyst, engineer, or instructor looking to interpret classic Förster's diagrams or apply them to modern systems, check out eddycurrent.com. It’s the only site that brings together history, training, tools, and modern interpretation of these foundational principles.

Need help figuring out what frequency to use?✅ 

Trying to understand why your array probe missed a defect?✅ 

Looking for side-by-side training resources?✅

It’s all there.

Final Thought

Dr. Förster's wasn’t just drawing spirals—he was building a map. Figure 1 is that map. And in today’s fast-paced world of AI-assisted testing and automation, understanding that map still gives you a crucial edge.

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