I'm considering to buy a new frame to replace my old and defected Merida Big Seven 100 27.5" MTB frame. I'm going to buy the new frame online as the store is very far from me. I couldn't make any sense of the dimensions they provide for the headset which is ø28.6ø41.8ø52*ø30, H:13mm.
I took the measure of the diameter of bearings of my current headset. It is around 38 mm for both top and bottom one. The fork is a SR Suntour 27 XCM HLO 100.
Attached is the photo of the frame I consider to buy
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The proposed frame is designed for a fork with a tapered steer tube, which is 1⅛" (28.6mm) at the top where the stem attaches, and at the fork crown, the steer tube has grown to 1½" (or nearly 40mm). As mentioned in the comments, one can fit a fork with an 1⅛" straight steer tube in a frame designed for a tapered steer tube by installing a special reducer fork crown race on the straight steer tube fork. The "reducing" aspect is that it allows the use of the larger bearing within the lower headtube (designed for tapered forks that measure 1½" at the crown) to fit nicely on the straight 1⅛" steer tube.
What's interesting about your online bike frame and their stated headset is the numbers they give imply that they are providing a reducer crown race with their headset. See, the other dimensions are for a tapered headtube (and that is what is shown in your photo) except for the ∅52*∅30. The 30 refers to a crown race sized for a straight, 1⅛" steer tube. A headset for a tapered head tube/tapered fork would read 52/40. I realize this may be confusing. The numbers the bike manufacturer gives for the the headset represent a partial version of what's known as Standardized Headset Identification System (SHIS). This is a way for various manufacturers of bikes and the various providers of headsets to speak a common language in regard to what headset is required for any particular bike. It also has information regarding the required size and type (straight or tapered) of fork steerer tube will work the headset & frame.
I'm going to refer you to a website tutorial that handles this topic very clearly. The lowdown on headset nomenclature is given by Park Tool in their S.H.I.S. Headset Identification System tutorial. Essentially, the letters within the SHIS refers to a type of headset and that is dependent on the design of a bike's head tube. The numbers represent the diameters of the pertinent parts involved, namely, the internal diameter of the bike headtube (coincides with the outside diameter of the cartridge bearing used at that part of the headtube) and the outside diameter of the fork steer tube or crown race seat of the steer tube (the lowest part of the steerer tube, exposed just above the fork crown). These measurements coincide with the internal diameter of the cartridge bearing used at the upper and lower head tube respectively.
To sum up, the numbers given by the bike manufacturer in your photo translate into SHIS form as: IS42/28.6|IS52/30. If you read the tutorial I linked to, you'll learn the first set of letters/numbers represent the upper headset (41.8 is rounded to 42 in SHIS), while the second set speak to the bottom (the 30 is a rounded up 28.7 and is actually very nearly the outer diameter of the lowest part of the steer tube--aka crown race seat, as well as the inner diameter of the crown race). The H:13 is the stack height in millimeters of that portion of the headset.
