In most of my operational squadrons we used to joke, "A pro never takes it around," always preaching just the opposite. But if that is really the case, having flown in some pretty rotten weather over the years, why is it that I've only really had to go missed a handful of times?
We do this routinely in the simulator but in real life it can come as a shock:
"Minimums, go around."
"Go around? What do you mean go around?"
Given that the actual call may come as a rude surprise, we need to treat it as the life and death decision that it is. There is nothing smooth about the missed approach at minimums, you need to do everything right and you need to do it immediately.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
[Instrument Flying Handbook pg. 10-22]
Things have gotten better with modern day flight management systems, you just need to make sure the FMS is programmed to do what you want and what ATC expects. If you are doing an approach that has a simultaneous approach to a parallel runway, there is an excellent chance the published missed approach procedure is not what is in your box. Realize too that your first turn following a circling approach may not necesarily be toward the approach runway when flying internationally. See International Operations / U.S. FAA verus ICAO Differences for more about this.
[Instrument Procedures Handbook pg. 5-29]
Just because you can see the runway doesn't mean you can land on that runway. See Normal Procedures & Techniques / Stabilized Approach for more about this.
Figure: Climbing or Missed Approach Required Obstacle Clearance, from TERPS Chap. 2, ¶ 202b.
[Aeronautical Information Manual ¶5-4-21.b.] Obstacle protection for missed approach is predicated on the missed approach being initiated at the decision altitude/height (DA/H) or at the missed approach point and not lower than minimum descent altitude (MDA). A climb gradient of at least 200 feet per nautical mile is required, (except for Copter approaches, where a climb of at least 400 feet per nautical mile is required), unless a higher climb gradient is published in the notes section of the approach procedure chart. When higher than standard climb gradients are specified, the end point of the non−standard climb will be specified at either an altitude or a fix. Pilots must preplan to ensure that the aircraft can meet the climb gradient (expressed in feet per nautical mile) required by the procedure in the event of a missed approach, and be aware that flying at a higher than anticipated ground speed increases the climb rate requirement (feet per minute). Tables for the conversion of climb gradients (feet per nautical mile) to climb rate (feet per minute), based on ground speed, are included on page D1 of the U.S. Terminal Procedures booklets. Reasonable buffers are provided for normal maneuvers. However, no consideration is given to an abnormally early turn. Therefore, when an early missed approach is executed, pilots should, unless otherwise cleared by ATC, fly the IAP as specified on the approach plate to the missed approach point at or above the MDA or DH before executing a turning maneuver.
[TERPS Chap. 2, ¶ 202b.] Climbing on departure or missed approach. The concept of providing obstacle clearance in the climb segment, in instrument procedures, is based on the aircraft maintaining a minimum climb gradient. The climb gradient must be sufficient to increase obstacle clearance along the flightpath so that the minimum ROC for the subsequent segment is achieved prior to leaving the climb segment (see figure 1-3). For TERPS purposes, the MINIMUM climb gradient that will provide adequate ROC in the climb segment is 200 ft/NM.
(1) The obstacle evaluation method for a climb segment is the application of a rising OCS below the minimum climbing flightpath. Whether the climb is for departure or missed approach is immaterial. The vertical distance between the climbing flightpath and the OCS is ROC. ROC for a climbing segment is defined as ROC = 0.24 CG. This concept is often called the 24% rule. Altitude gained is dependent on climb gradient (CG) expressed in feet per NM. The minimum ROC supplied by the 200 ft/NM CG is 48 ft/NM (0.24 × 200 = 48). Since 48 of the 200 feet gained in 1 NM is ROC, the OCS height at that point must be 152 feet (200 - 48 = 152), or 76% of the CG (152 ÷ 200 = 0.76). The slope of a surface that rises 152 over 1 NM is 40 (6076.11548 ÷ 152 = 39.97 = 40).
(2) Where an obstruction penetrates the OCS, a nonstandard climb gradient (greater than 200 ft/NM) is required to provide adequate ROC. Since the climb gradient will be greater than 200 ft/NM, ROC will be greater than 48 ft/NM (0.24 X CG > 200 = ROC > 48). The nonstandard ROC expressed in ft/NM can be calculated using the formula: (0.24 h) ÷ (0.76 d) where "h" is the height of the obstacle above the altitude from which the climb is initiated, and "d" is the distance in NM from the initiation of climb to the obstacle. Normally, instead of calculating the nonstandard ROC value, the required climb gradient is calculated directly using the formula: h ÷ (0.76d).
[TERPS Chap. 2, ¶ 202d.] In the case of a missed approach procedure, the climbing flight path starts at the height of MDA or DA minus height loss. The OCS starts approximately at the MAP/DA point at an altitude of MDA/DA minus the final segment ROC and adjustments. Therefore, the final segment ROC is assured at the beginning of the OCS, and increases as the missed approach route progresses. The OCS is applied until at least the minimum initial or en route value of ROC is attained, as appropriate.
No, you don't need math to fly a missed approach. The point here is that there isn't a lot of obstacle clearance and the sooner you climb, the better. While you must follow the ground track of the approach until the missed approach point, nothing precludes you from making an earlier climb.
FAA-H-8083-15, Instrument Flying Handbook, U.S. Department of Transportation, Flight Standards Service, 2001.
FAA-H-8261-1, Instrument Procedures Handbook, U.S. Department of Transportation, Flight Standards Branch, 2004
United States Standard for Terminal Instrument Procedures (TERPS), Federal Aviation Administration 8260.3B CHG 19, 5/15/02